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<FONT color="green">001</FONT>    // CHECKSTYLE: stop all<a name="line.1"></a>
<FONT color="green">002</FONT>    /*<a name="line.2"></a>
<FONT color="green">003</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.3"></a>
<FONT color="green">004</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.4"></a>
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<FONT color="green">008</FONT>     * the License.  You may obtain a copy of the License at<a name="line.8"></a>
<FONT color="green">009</FONT>     *<a name="line.9"></a>
<FONT color="green">010</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.10"></a>
<FONT color="green">011</FONT>     *<a name="line.11"></a>
<FONT color="green">012</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.12"></a>
<FONT color="green">013</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.13"></a>
<FONT color="green">014</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.14"></a>
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<FONT color="green">016</FONT>     * limitations under the License.<a name="line.16"></a>
<FONT color="green">017</FONT>     */<a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math3.optim.nonlinear.scalar.noderiv;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import java.util.Arrays;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.MathIllegalStateException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.NumberIsTooSmallException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.exception.OutOfRangeException;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.linear.Array2DRowRealMatrix;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.linear.ArrayRealVector;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.linear.RealVector;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.optim.nonlinear.scalar.GoalType;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.optim.PointValuePair;<a name="line.29"></a>
<FONT color="green">030</FONT>    import org.apache.commons.math3.optim.nonlinear.scalar.MultivariateOptimizer;<a name="line.30"></a>
<FONT color="green">031</FONT>    <a name="line.31"></a>
<FONT color="green">032</FONT>    /**<a name="line.32"></a>
<FONT color="green">033</FONT>     * Powell's BOBYQA algorithm. This implementation is translated and<a name="line.33"></a>
<FONT color="green">034</FONT>     * adapted from the Fortran version available<a name="line.34"></a>
<FONT color="green">035</FONT>     * &lt;a href="http://plato.asu.edu/ftp/other_software/bobyqa.zip"&gt;here&lt;/a&gt;.<a name="line.35"></a>
<FONT color="green">036</FONT>     * See &lt;a href="http://www.optimization-online.org/DB_HTML/2010/05/2616.html"&gt;<a name="line.36"></a>
<FONT color="green">037</FONT>     * this paper&lt;/a&gt; for an introduction.<a name="line.37"></a>
<FONT color="green">038</FONT>     * &lt;br/&gt;<a name="line.38"></a>
<FONT color="green">039</FONT>     * BOBYQA is particularly well suited for high dimensional problems<a name="line.39"></a>
<FONT color="green">040</FONT>     * where derivatives are not available. In most cases it outperforms the<a name="line.40"></a>
<FONT color="green">041</FONT>     * {@link PowellOptimizer} significantly. Stochastic algorithms like<a name="line.41"></a>
<FONT color="green">042</FONT>     * {@link CMAESOptimizer} succeed more often than BOBYQA, but are more<a name="line.42"></a>
<FONT color="green">043</FONT>     * expensive. BOBYQA could also be considered as a replacement of any<a name="line.43"></a>
<FONT color="green">044</FONT>     * derivative-based optimizer when the derivatives are approximated by<a name="line.44"></a>
<FONT color="green">045</FONT>     * finite differences.<a name="line.45"></a>
<FONT color="green">046</FONT>     *<a name="line.46"></a>
<FONT color="green">047</FONT>     * @version $Id: BOBYQAOptimizer.java 1413131 2012-11-24 04:44:02Z psteitz $<a name="line.47"></a>
<FONT color="green">048</FONT>     * @since 3.0<a name="line.48"></a>
<FONT color="green">049</FONT>     */<a name="line.49"></a>
<FONT color="green">050</FONT>    public class BOBYQAOptimizer<a name="line.50"></a>
<FONT color="green">051</FONT>        extends MultivariateOptimizer {<a name="line.51"></a>
<FONT color="green">052</FONT>        /** Minimum dimension of the problem: {@value} */<a name="line.52"></a>
<FONT color="green">053</FONT>        public static final int MINIMUM_PROBLEM_DIMENSION = 2;<a name="line.53"></a>
<FONT color="green">054</FONT>        /** Default value for {@link #initialTrustRegionRadius}: {@value} . */<a name="line.54"></a>
<FONT color="green">055</FONT>        public static final double DEFAULT_INITIAL_RADIUS = 10.0;<a name="line.55"></a>
<FONT color="green">056</FONT>        /** Default value for {@link #stoppingTrustRegionRadius}: {@value} . */<a name="line.56"></a>
<FONT color="green">057</FONT>        public static final double DEFAULT_STOPPING_RADIUS = 1E-8;<a name="line.57"></a>
<FONT color="green">058</FONT>    <a name="line.58"></a>
<FONT color="green">059</FONT>        private static final double ZERO = 0d;<a name="line.59"></a>
<FONT color="green">060</FONT>        private static final double ONE = 1d;<a name="line.60"></a>
<FONT color="green">061</FONT>        private static final double TWO = 2d;<a name="line.61"></a>
<FONT color="green">062</FONT>        private static final double TEN = 10d;<a name="line.62"></a>
<FONT color="green">063</FONT>        private static final double SIXTEEN = 16d;<a name="line.63"></a>
<FONT color="green">064</FONT>        private static final double TWO_HUNDRED_FIFTY = 250d;<a name="line.64"></a>
<FONT color="green">065</FONT>        private static final double MINUS_ONE = -ONE;<a name="line.65"></a>
<FONT color="green">066</FONT>        private static final double HALF = ONE / 2;<a name="line.66"></a>
<FONT color="green">067</FONT>        private static final double ONE_OVER_FOUR = ONE / 4;<a name="line.67"></a>
<FONT color="green">068</FONT>        private static final double ONE_OVER_EIGHT = ONE / 8;<a name="line.68"></a>
<FONT color="green">069</FONT>        private static final double ONE_OVER_TEN = ONE / 10;<a name="line.69"></a>
<FONT color="green">070</FONT>        private static final double ONE_OVER_A_THOUSAND = ONE / 1000;<a name="line.70"></a>
<FONT color="green">071</FONT>    <a name="line.71"></a>
<FONT color="green">072</FONT>        /**<a name="line.72"></a>
<FONT color="green">073</FONT>         * numberOfInterpolationPoints XXX<a name="line.73"></a>
<FONT color="green">074</FONT>         */<a name="line.74"></a>
<FONT color="green">075</FONT>        private final int numberOfInterpolationPoints;<a name="line.75"></a>
<FONT color="green">076</FONT>        /**<a name="line.76"></a>
<FONT color="green">077</FONT>         * initialTrustRegionRadius XXX<a name="line.77"></a>
<FONT color="green">078</FONT>         */<a name="line.78"></a>
<FONT color="green">079</FONT>        private double initialTrustRegionRadius;<a name="line.79"></a>
<FONT color="green">080</FONT>        /**<a name="line.80"></a>
<FONT color="green">081</FONT>         * stoppingTrustRegionRadius XXX<a name="line.81"></a>
<FONT color="green">082</FONT>         */<a name="line.82"></a>
<FONT color="green">083</FONT>        private final double stoppingTrustRegionRadius;<a name="line.83"></a>
<FONT color="green">084</FONT>        /** Goal type (minimize or maximize). */<a name="line.84"></a>
<FONT color="green">085</FONT>        private boolean isMinimize;<a name="line.85"></a>
<FONT color="green">086</FONT>        /**<a name="line.86"></a>
<FONT color="green">087</FONT>         * Current best values for the variables to be optimized.<a name="line.87"></a>
<FONT color="green">088</FONT>         * The vector will be changed in-place to contain the values of the least<a name="line.88"></a>
<FONT color="green">089</FONT>         * calculated objective function values.<a name="line.89"></a>
<FONT color="green">090</FONT>         */<a name="line.90"></a>
<FONT color="green">091</FONT>        private ArrayRealVector currentBest;<a name="line.91"></a>
<FONT color="green">092</FONT>        /** Differences between the upper and lower bounds. */<a name="line.92"></a>
<FONT color="green">093</FONT>        private double[] boundDifference;<a name="line.93"></a>
<FONT color="green">094</FONT>        /**<a name="line.94"></a>
<FONT color="green">095</FONT>         * Index of the interpolation point at the trust region center.<a name="line.95"></a>
<FONT color="green">096</FONT>         */<a name="line.96"></a>
<FONT color="green">097</FONT>        private int trustRegionCenterInterpolationPointIndex;<a name="line.97"></a>
<FONT color="green">098</FONT>        /**<a name="line.98"></a>
<FONT color="green">099</FONT>         * Last &lt;em&gt;n&lt;/em&gt; columns of matrix H (where &lt;em&gt;n&lt;/em&gt; is the dimension<a name="line.99"></a>
<FONT color="green">100</FONT>         * of the problem).<a name="line.100"></a>
<FONT color="green">101</FONT>         * XXX "bmat" in the original code.<a name="line.101"></a>
<FONT color="green">102</FONT>         */<a name="line.102"></a>
<FONT color="green">103</FONT>        private Array2DRowRealMatrix bMatrix;<a name="line.103"></a>
<FONT color="green">104</FONT>        /**<a name="line.104"></a>
<FONT color="green">105</FONT>         * Factorization of the leading &lt;em&gt;npt&lt;/em&gt; square submatrix of H, this<a name="line.105"></a>
<FONT color="green">106</FONT>         * factorization being Z Z&lt;sup&gt;T&lt;/sup&gt;, which provides both the correct<a name="line.106"></a>
<FONT color="green">107</FONT>         * rank and positive semi-definiteness.<a name="line.107"></a>
<FONT color="green">108</FONT>         * XXX "zmat" in the original code.<a name="line.108"></a>
<FONT color="green">109</FONT>         */<a name="line.109"></a>
<FONT color="green">110</FONT>        private Array2DRowRealMatrix zMatrix;<a name="line.110"></a>
<FONT color="green">111</FONT>        /**<a name="line.111"></a>
<FONT color="green">112</FONT>         * Coordinates of the interpolation points relative to {@link #originShift}.<a name="line.112"></a>
<FONT color="green">113</FONT>         * XXX "xpt" in the original code.<a name="line.113"></a>
<FONT color="green">114</FONT>         */<a name="line.114"></a>
<FONT color="green">115</FONT>        private Array2DRowRealMatrix interpolationPoints;<a name="line.115"></a>
<FONT color="green">116</FONT>        /**<a name="line.116"></a>
<FONT color="green">117</FONT>         * Shift of origin that should reduce the contributions from rounding<a name="line.117"></a>
<FONT color="green">118</FONT>         * errors to values of the model and Lagrange functions.<a name="line.118"></a>
<FONT color="green">119</FONT>         * XXX "xbase" in the original code.<a name="line.119"></a>
<FONT color="green">120</FONT>         */<a name="line.120"></a>
<FONT color="green">121</FONT>        private ArrayRealVector originShift;<a name="line.121"></a>
<FONT color="green">122</FONT>        /**<a name="line.122"></a>
<FONT color="green">123</FONT>         * Values of the objective function at the interpolation points.<a name="line.123"></a>
<FONT color="green">124</FONT>         * XXX "fval" in the original code.<a name="line.124"></a>
<FONT color="green">125</FONT>         */<a name="line.125"></a>
<FONT color="green">126</FONT>        private ArrayRealVector fAtInterpolationPoints;<a name="line.126"></a>
<FONT color="green">127</FONT>        /**<a name="line.127"></a>
<FONT color="green">128</FONT>         * Displacement from {@link #originShift} of the trust region center.<a name="line.128"></a>
<FONT color="green">129</FONT>         * XXX "xopt" in the original code.<a name="line.129"></a>
<FONT color="green">130</FONT>         */<a name="line.130"></a>
<FONT color="green">131</FONT>        private ArrayRealVector trustRegionCenterOffset;<a name="line.131"></a>
<FONT color="green">132</FONT>        /**<a name="line.132"></a>
<FONT color="green">133</FONT>         * Gradient of the quadratic model at {@link #originShift} +<a name="line.133"></a>
<FONT color="green">134</FONT>         * {@link #trustRegionCenterOffset}.<a name="line.134"></a>
<FONT color="green">135</FONT>         * XXX "gopt" in the original code.<a name="line.135"></a>
<FONT color="green">136</FONT>         */<a name="line.136"></a>
<FONT color="green">137</FONT>        private ArrayRealVector gradientAtTrustRegionCenter;<a name="line.137"></a>
<FONT color="green">138</FONT>        /**<a name="line.138"></a>
<FONT color="green">139</FONT>         * Differences {@link #getLowerBound()} - {@link #originShift}.<a name="line.139"></a>
<FONT color="green">140</FONT>         * All the components of every {@link #trustRegionCenterOffset} are going<a name="line.140"></a>
<FONT color="green">141</FONT>         * to satisfy the bounds&lt;br/&gt;<a name="line.141"></a>
<FONT color="green">142</FONT>         * {@link #getLowerBound() lowerBound}&lt;sub&gt;i&lt;/sub&gt; &amp;le;<a name="line.142"></a>
<FONT color="green">143</FONT>         * {@link #trustRegionCenterOffset}&lt;sub&gt;i&lt;/sub&gt;,&lt;br/&gt;<a name="line.143"></a>
<FONT color="green">144</FONT>         * with appropriate equalities when {@link #trustRegionCenterOffset} is<a name="line.144"></a>
<FONT color="green">145</FONT>         * on a constraint boundary.<a name="line.145"></a>
<FONT color="green">146</FONT>         * XXX "sl" in the original code.<a name="line.146"></a>
<FONT color="green">147</FONT>         */<a name="line.147"></a>
<FONT color="green">148</FONT>        private ArrayRealVector lowerDifference;<a name="line.148"></a>
<FONT color="green">149</FONT>        /**<a name="line.149"></a>
<FONT color="green">150</FONT>         * Differences {@link #getUpperBound()} - {@link #originShift}<a name="line.150"></a>
<FONT color="green">151</FONT>         * All the components of every {@link #trustRegionCenterOffset} are going<a name="line.151"></a>
<FONT color="green">152</FONT>         * to satisfy the bounds&lt;br/&gt;<a name="line.152"></a>
<FONT color="green">153</FONT>         *  {@link #trustRegionCenterOffset}&lt;sub&gt;i&lt;/sub&gt; &amp;le;<a name="line.153"></a>
<FONT color="green">154</FONT>         *  {@link #getUpperBound() upperBound}&lt;sub&gt;i&lt;/sub&gt;,&lt;br/&gt;<a name="line.154"></a>
<FONT color="green">155</FONT>         * with appropriate equalities when {@link #trustRegionCenterOffset} is<a name="line.155"></a>
<FONT color="green">156</FONT>         * on a constraint boundary.<a name="line.156"></a>
<FONT color="green">157</FONT>         * XXX "su" in the original code.<a name="line.157"></a>
<FONT color="green">158</FONT>         */<a name="line.158"></a>
<FONT color="green">159</FONT>        private ArrayRealVector upperDifference;<a name="line.159"></a>
<FONT color="green">160</FONT>        /**<a name="line.160"></a>
<FONT color="green">161</FONT>         * Parameters of the implicit second derivatives of the quadratic model.<a name="line.161"></a>
<FONT color="green">162</FONT>         * XXX "pq" in the original code.<a name="line.162"></a>
<FONT color="green">163</FONT>         */<a name="line.163"></a>
<FONT color="green">164</FONT>        private ArrayRealVector modelSecondDerivativesParameters;<a name="line.164"></a>
<FONT color="green">165</FONT>        /**<a name="line.165"></a>
<FONT color="green">166</FONT>         * Point chosen by function {@link #trsbox(double,ArrayRealVector,<a name="line.166"></a>
<FONT color="green">167</FONT>         * ArrayRealVector, ArrayRealVector,ArrayRealVector,ArrayRealVector) trsbox}<a name="line.167"></a>
<FONT color="green">168</FONT>         * or {@link #altmov(int,double) altmov}.<a name="line.168"></a>
<FONT color="green">169</FONT>         * Usually {@link #originShift} + {@link #newPoint} is the vector of<a name="line.169"></a>
<FONT color="green">170</FONT>         * variables for the next evaluation of the objective function.<a name="line.170"></a>
<FONT color="green">171</FONT>         * It also satisfies the constraints indicated in {@link #lowerDifference}<a name="line.171"></a>
<FONT color="green">172</FONT>         * and {@link #upperDifference}.<a name="line.172"></a>
<FONT color="green">173</FONT>         * XXX "xnew" in the original code.<a name="line.173"></a>
<FONT color="green">174</FONT>         */<a name="line.174"></a>
<FONT color="green">175</FONT>        private ArrayRealVector newPoint;<a name="line.175"></a>
<FONT color="green">176</FONT>        /**<a name="line.176"></a>
<FONT color="green">177</FONT>         * Alternative to {@link #newPoint}, chosen by<a name="line.177"></a>
<FONT color="green">178</FONT>         * {@link #altmov(int,double) altmov}.<a name="line.178"></a>
<FONT color="green">179</FONT>         * It may replace {@link #newPoint} in order to increase the denominator<a name="line.179"></a>
<FONT color="green">180</FONT>         * in the {@link #update(double, double, int) updating procedure}.<a name="line.180"></a>
<FONT color="green">181</FONT>         * XXX "xalt" in the original code.<a name="line.181"></a>
<FONT color="green">182</FONT>         */<a name="line.182"></a>
<FONT color="green">183</FONT>        private ArrayRealVector alternativeNewPoint;<a name="line.183"></a>
<FONT color="green">184</FONT>        /**<a name="line.184"></a>
<FONT color="green">185</FONT>         * Trial step from {@link #trustRegionCenterOffset} which is usually<a name="line.185"></a>
<FONT color="green">186</FONT>         * {@link #newPoint} - {@link #trustRegionCenterOffset}.<a name="line.186"></a>
<FONT color="green">187</FONT>         * XXX "d__" in the original code.<a name="line.187"></a>
<FONT color="green">188</FONT>         */<a name="line.188"></a>
<FONT color="green">189</FONT>        private ArrayRealVector trialStepPoint;<a name="line.189"></a>
<FONT color="green">190</FONT>        /**<a name="line.190"></a>
<FONT color="green">191</FONT>         * Values of the Lagrange functions at a new point.<a name="line.191"></a>
<FONT color="green">192</FONT>         * XXX "vlag" in the original code.<a name="line.192"></a>
<FONT color="green">193</FONT>         */<a name="line.193"></a>
<FONT color="green">194</FONT>        private ArrayRealVector lagrangeValuesAtNewPoint;<a name="line.194"></a>
<FONT color="green">195</FONT>        /**<a name="line.195"></a>
<FONT color="green">196</FONT>         * Explicit second derivatives of the quadratic model.<a name="line.196"></a>
<FONT color="green">197</FONT>         * XXX "hq" in the original code.<a name="line.197"></a>
<FONT color="green">198</FONT>         */<a name="line.198"></a>
<FONT color="green">199</FONT>        private ArrayRealVector modelSecondDerivativesValues;<a name="line.199"></a>
<FONT color="green">200</FONT>    <a name="line.200"></a>
<FONT color="green">201</FONT>        /**<a name="line.201"></a>
<FONT color="green">202</FONT>         * @param numberOfInterpolationPoints Number of interpolation conditions.<a name="line.202"></a>
<FONT color="green">203</FONT>         * For a problem of dimension {@code n}, its value must be in the interval<a name="line.203"></a>
<FONT color="green">204</FONT>         * {@code [n+2, (n+1)(n+2)/2]}.<a name="line.204"></a>
<FONT color="green">205</FONT>         * Choices that exceed {@code 2n+1} are not recommended.<a name="line.205"></a>
<FONT color="green">206</FONT>         */<a name="line.206"></a>
<FONT color="green">207</FONT>        public BOBYQAOptimizer(int numberOfInterpolationPoints) {<a name="line.207"></a>
<FONT color="green">208</FONT>            this(numberOfInterpolationPoints,<a name="line.208"></a>
<FONT color="green">209</FONT>                 DEFAULT_INITIAL_RADIUS,<a name="line.209"></a>
<FONT color="green">210</FONT>                 DEFAULT_STOPPING_RADIUS);<a name="line.210"></a>
<FONT color="green">211</FONT>        }<a name="line.211"></a>
<FONT color="green">212</FONT>    <a name="line.212"></a>
<FONT color="green">213</FONT>        /**<a name="line.213"></a>
<FONT color="green">214</FONT>         * @param numberOfInterpolationPoints Number of interpolation conditions.<a name="line.214"></a>
<FONT color="green">215</FONT>         * For a problem of dimension {@code n}, its value must be in the interval<a name="line.215"></a>
<FONT color="green">216</FONT>         * {@code [n+2, (n+1)(n+2)/2]}.<a name="line.216"></a>
<FONT color="green">217</FONT>         * Choices that exceed {@code 2n+1} are not recommended.<a name="line.217"></a>
<FONT color="green">218</FONT>         * @param initialTrustRegionRadius Initial trust region radius.<a name="line.218"></a>
<FONT color="green">219</FONT>         * @param stoppingTrustRegionRadius Stopping trust region radius.<a name="line.219"></a>
<FONT color="green">220</FONT>         */<a name="line.220"></a>
<FONT color="green">221</FONT>        public BOBYQAOptimizer(int numberOfInterpolationPoints,<a name="line.221"></a>
<FONT color="green">222</FONT>                               double initialTrustRegionRadius,<a name="line.222"></a>
<FONT color="green">223</FONT>                               double stoppingTrustRegionRadius) {<a name="line.223"></a>
<FONT color="green">224</FONT>            super(null); // No custom convergence criterion.<a name="line.224"></a>
<FONT color="green">225</FONT>            this.numberOfInterpolationPoints = numberOfInterpolationPoints;<a name="line.225"></a>
<FONT color="green">226</FONT>            this.initialTrustRegionRadius = initialTrustRegionRadius;<a name="line.226"></a>
<FONT color="green">227</FONT>            this.stoppingTrustRegionRadius = stoppingTrustRegionRadius;<a name="line.227"></a>
<FONT color="green">228</FONT>        }<a name="line.228"></a>
<FONT color="green">229</FONT>    <a name="line.229"></a>
<FONT color="green">230</FONT>        /** {@inheritDoc} */<a name="line.230"></a>
<FONT color="green">231</FONT>        @Override<a name="line.231"></a>
<FONT color="green">232</FONT>        protected PointValuePair doOptimize() {<a name="line.232"></a>
<FONT color="green">233</FONT>            final double[] lowerBound = getLowerBound();<a name="line.233"></a>
<FONT color="green">234</FONT>            final double[] upperBound = getUpperBound();<a name="line.234"></a>
<FONT color="green">235</FONT>    <a name="line.235"></a>
<FONT color="green">236</FONT>            // Validity checks.<a name="line.236"></a>
<FONT color="green">237</FONT>            setup(lowerBound, upperBound);<a name="line.237"></a>
<FONT color="green">238</FONT>    <a name="line.238"></a>
<FONT color="green">239</FONT>            isMinimize = (getGoalType() == GoalType.MINIMIZE);<a name="line.239"></a>
<FONT color="green">240</FONT>            currentBest = new ArrayRealVector(getStartPoint());<a name="line.240"></a>
<FONT color="green">241</FONT>    <a name="line.241"></a>
<FONT color="green">242</FONT>            final double value = bobyqa(lowerBound, upperBound);<a name="line.242"></a>
<FONT color="green">243</FONT>    <a name="line.243"></a>
<FONT color="green">244</FONT>            return new PointValuePair(currentBest.getDataRef(),<a name="line.244"></a>
<FONT color="green">245</FONT>                                      isMinimize ? value : -value);<a name="line.245"></a>
<FONT color="green">246</FONT>        }<a name="line.246"></a>
<FONT color="green">247</FONT>    <a name="line.247"></a>
<FONT color="green">248</FONT>        /**<a name="line.248"></a>
<FONT color="green">249</FONT>         *     This subroutine seeks the least value of a function of many variables,<a name="line.249"></a>
<FONT color="green">250</FONT>         *     by applying a trust region method that forms quadratic models by<a name="line.250"></a>
<FONT color="green">251</FONT>         *     interpolation. There is usually some freedom in the interpolation<a name="line.251"></a>
<FONT color="green">252</FONT>         *     conditions, which is taken up by minimizing the Frobenius norm of<a name="line.252"></a>
<FONT color="green">253</FONT>         *     the change to the second derivative of the model, beginning with the<a name="line.253"></a>
<FONT color="green">254</FONT>         *     zero matrix. The values of the variables are constrained by upper and<a name="line.254"></a>
<FONT color="green">255</FONT>         *     lower bounds. The arguments of the subroutine are as follows.<a name="line.255"></a>
<FONT color="green">256</FONT>         *<a name="line.256"></a>
<FONT color="green">257</FONT>         *     N must be set to the number of variables and must be at least two.<a name="line.257"></a>
<FONT color="green">258</FONT>         *     NPT is the number of interpolation conditions. Its value must be in<a name="line.258"></a>
<FONT color="green">259</FONT>         *       the interval [N+2,(N+1)(N+2)/2]. Choices that exceed 2*N+1 are not<a name="line.259"></a>
<FONT color="green">260</FONT>         *       recommended.<a name="line.260"></a>
<FONT color="green">261</FONT>         *     Initial values of the variables must be set in X(1),X(2),...,X(N). They<a name="line.261"></a>
<FONT color="green">262</FONT>         *       will be changed to the values that give the least calculated F.<a name="line.262"></a>
<FONT color="green">263</FONT>         *     For I=1,2,...,N, XL(I) and XU(I) must provide the lower and upper<a name="line.263"></a>
<FONT color="green">264</FONT>         *       bounds, respectively, on X(I). The construction of quadratic models<a name="line.264"></a>
<FONT color="green">265</FONT>         *       requires XL(I) to be strictly less than XU(I) for each I. Further,<a name="line.265"></a>
<FONT color="green">266</FONT>         *       the contribution to a model from changes to the I-th variable is<a name="line.266"></a>
<FONT color="green">267</FONT>         *       damaged severely by rounding errors if XU(I)-XL(I) is too small.<a name="line.267"></a>
<FONT color="green">268</FONT>         *     RHOBEG and RHOEND must be set to the initial and final values of a trust<a name="line.268"></a>
<FONT color="green">269</FONT>         *       region radius, so both must be positive with RHOEND no greater than<a name="line.269"></a>
<FONT color="green">270</FONT>         *       RHOBEG. Typically, RHOBEG should be about one tenth of the greatest<a name="line.270"></a>
<FONT color="green">271</FONT>         *       expected change to a variable, while RHOEND should indicate the<a name="line.271"></a>
<FONT color="green">272</FONT>         *       accuracy that is required in the final values of the variables. An<a name="line.272"></a>
<FONT color="green">273</FONT>         *       error return occurs if any of the differences XU(I)-XL(I), I=1,...,N,<a name="line.273"></a>
<FONT color="green">274</FONT>         *       is less than 2*RHOBEG.<a name="line.274"></a>
<FONT color="green">275</FONT>         *     MAXFUN must be set to an upper bound on the number of calls of CALFUN.<a name="line.275"></a>
<FONT color="green">276</FONT>         *     The array W will be used for working space. Its length must be at least<a name="line.276"></a>
<FONT color="green">277</FONT>         *       (NPT+5)*(NPT+N)+3*N*(N+5)/2.<a name="line.277"></a>
<FONT color="green">278</FONT>         *<a name="line.278"></a>
<FONT color="green">279</FONT>         * @param lowerBound Lower bounds.<a name="line.279"></a>
<FONT color="green">280</FONT>         * @param upperBound Upper bounds.<a name="line.280"></a>
<FONT color="green">281</FONT>         * @return the value of the objective at the optimum.<a name="line.281"></a>
<FONT color="green">282</FONT>         */<a name="line.282"></a>
<FONT color="green">283</FONT>        private double bobyqa(double[] lowerBound,<a name="line.283"></a>
<FONT color="green">284</FONT>                              double[] upperBound) {<a name="line.284"></a>
<FONT color="green">285</FONT>            printMethod(); // XXX<a name="line.285"></a>
<FONT color="green">286</FONT>    <a name="line.286"></a>
<FONT color="green">287</FONT>            final int n = currentBest.getDimension();<a name="line.287"></a>
<FONT color="green">288</FONT>    <a name="line.288"></a>
<FONT color="green">289</FONT>            // Return if there is insufficient space between the bounds. Modify the<a name="line.289"></a>
<FONT color="green">290</FONT>            // initial X if necessary in order to avoid conflicts between the bounds<a name="line.290"></a>
<FONT color="green">291</FONT>            // and the construction of the first quadratic model. The lower and upper<a name="line.291"></a>
<FONT color="green">292</FONT>            // bounds on moves from the updated X are set now, in the ISL and ISU<a name="line.292"></a>
<FONT color="green">293</FONT>            // partitions of W, in order to provide useful and exact information about<a name="line.293"></a>
<FONT color="green">294</FONT>            // components of X that become within distance RHOBEG from their bounds.<a name="line.294"></a>
<FONT color="green">295</FONT>    <a name="line.295"></a>
<FONT color="green">296</FONT>            for (int j = 0; j &lt; n; j++) {<a name="line.296"></a>
<FONT color="green">297</FONT>                final double boundDiff = boundDifference[j];<a name="line.297"></a>
<FONT color="green">298</FONT>                lowerDifference.setEntry(j, lowerBound[j] - currentBest.getEntry(j));<a name="line.298"></a>
<FONT color="green">299</FONT>                upperDifference.setEntry(j, upperBound[j] - currentBest.getEntry(j));<a name="line.299"></a>
<FONT color="green">300</FONT>                if (lowerDifference.getEntry(j) &gt;= -initialTrustRegionRadius) {<a name="line.300"></a>
<FONT color="green">301</FONT>                    if (lowerDifference.getEntry(j) &gt;= ZERO) {<a name="line.301"></a>
<FONT color="green">302</FONT>                        currentBest.setEntry(j, lowerBound[j]);<a name="line.302"></a>
<FONT color="green">303</FONT>                        lowerDifference.setEntry(j, ZERO);<a name="line.303"></a>
<FONT color="green">304</FONT>                        upperDifference.setEntry(j, boundDiff);<a name="line.304"></a>
<FONT color="green">305</FONT>                    } else {<a name="line.305"></a>
<FONT color="green">306</FONT>                        currentBest.setEntry(j, lowerBound[j] + initialTrustRegionRadius);<a name="line.306"></a>
<FONT color="green">307</FONT>                        lowerDifference.setEntry(j, -initialTrustRegionRadius);<a name="line.307"></a>
<FONT color="green">308</FONT>                        // Computing MAX<a name="line.308"></a>
<FONT color="green">309</FONT>                        final double deltaOne = upperBound[j] - currentBest.getEntry(j);<a name="line.309"></a>
<FONT color="green">310</FONT>                        upperDifference.setEntry(j, Math.max(deltaOne, initialTrustRegionRadius));<a name="line.310"></a>
<FONT color="green">311</FONT>                    }<a name="line.311"></a>
<FONT color="green">312</FONT>                } else if (upperDifference.getEntry(j) &lt;= initialTrustRegionRadius) {<a name="line.312"></a>
<FONT color="green">313</FONT>                    if (upperDifference.getEntry(j) &lt;= ZERO) {<a name="line.313"></a>
<FONT color="green">314</FONT>                        currentBest.setEntry(j, upperBound[j]);<a name="line.314"></a>
<FONT color="green">315</FONT>                        lowerDifference.setEntry(j, -boundDiff);<a name="line.315"></a>
<FONT color="green">316</FONT>                        upperDifference.setEntry(j, ZERO);<a name="line.316"></a>
<FONT color="green">317</FONT>                    } else {<a name="line.317"></a>
<FONT color="green">318</FONT>                        currentBest.setEntry(j, upperBound[j] - initialTrustRegionRadius);<a name="line.318"></a>
<FONT color="green">319</FONT>                        // Computing MIN<a name="line.319"></a>
<FONT color="green">320</FONT>                        final double deltaOne = lowerBound[j] - currentBest.getEntry(j);<a name="line.320"></a>
<FONT color="green">321</FONT>                        final double deltaTwo = -initialTrustRegionRadius;<a name="line.321"></a>
<FONT color="green">322</FONT>                        lowerDifference.setEntry(j, Math.min(deltaOne, deltaTwo));<a name="line.322"></a>
<FONT color="green">323</FONT>                        upperDifference.setEntry(j, initialTrustRegionRadius);<a name="line.323"></a>
<FONT color="green">324</FONT>                    }<a name="line.324"></a>
<FONT color="green">325</FONT>                }<a name="line.325"></a>
<FONT color="green">326</FONT>            }<a name="line.326"></a>
<FONT color="green">327</FONT>    <a name="line.327"></a>
<FONT color="green">328</FONT>            // Make the call of BOBYQB.<a name="line.328"></a>
<FONT color="green">329</FONT>    <a name="line.329"></a>
<FONT color="green">330</FONT>            return bobyqb(lowerBound, upperBound);<a name="line.330"></a>
<FONT color="green">331</FONT>        } // bobyqa<a name="line.331"></a>
<FONT color="green">332</FONT>    <a name="line.332"></a>
<FONT color="green">333</FONT>        // ----------------------------------------------------------------------------------------<a name="line.333"></a>
<FONT color="green">334</FONT>    <a name="line.334"></a>
<FONT color="green">335</FONT>        /**<a name="line.335"></a>
<FONT color="green">336</FONT>         *     The arguments N, NPT, X, XL, XU, RHOBEG, RHOEND, IPRINT and MAXFUN<a name="line.336"></a>
<FONT color="green">337</FONT>         *       are identical to the corresponding arguments in SUBROUTINE BOBYQA.<a name="line.337"></a>
<FONT color="green">338</FONT>         *     XBASE holds a shift of origin that should reduce the contributions<a name="line.338"></a>
<FONT color="green">339</FONT>         *       from rounding errors to values of the model and Lagrange functions.<a name="line.339"></a>
<FONT color="green">340</FONT>         *     XPT is a two-dimensional array that holds the coordinates of the<a name="line.340"></a>
<FONT color="green">341</FONT>         *       interpolation points relative to XBASE.<a name="line.341"></a>
<FONT color="green">342</FONT>         *     FVAL holds the values of F at the interpolation points.<a name="line.342"></a>
<FONT color="green">343</FONT>         *     XOPT is set to the displacement from XBASE of the trust region centre.<a name="line.343"></a>
<FONT color="green">344</FONT>         *     GOPT holds the gradient of the quadratic model at XBASE+XOPT.<a name="line.344"></a>
<FONT color="green">345</FONT>         *     HQ holds the explicit second derivatives of the quadratic model.<a name="line.345"></a>
<FONT color="green">346</FONT>         *     PQ contains the parameters of the implicit second derivatives of the<a name="line.346"></a>
<FONT color="green">347</FONT>         *       quadratic model.<a name="line.347"></a>
<FONT color="green">348</FONT>         *     BMAT holds the last N columns of H.<a name="line.348"></a>
<FONT color="green">349</FONT>         *     ZMAT holds the factorization of the leading NPT by NPT submatrix of H,<a name="line.349"></a>
<FONT color="green">350</FONT>         *       this factorization being ZMAT times ZMAT^T, which provides both the<a name="line.350"></a>
<FONT color="green">351</FONT>         *       correct rank and positive semi-definiteness.<a name="line.351"></a>
<FONT color="green">352</FONT>         *     NDIM is the first dimension of BMAT and has the value NPT+N.<a name="line.352"></a>
<FONT color="green">353</FONT>         *     SL and SU hold the differences XL-XBASE and XU-XBASE, respectively.<a name="line.353"></a>
<FONT color="green">354</FONT>         *       All the components of every XOPT are going to satisfy the bounds<a name="line.354"></a>
<FONT color="green">355</FONT>         *       SL(I) .LEQ. XOPT(I) .LEQ. SU(I), with appropriate equalities when<a name="line.355"></a>
<FONT color="green">356</FONT>         *       XOPT is on a constraint boundary.<a name="line.356"></a>
<FONT color="green">357</FONT>         *     XNEW is chosen by SUBROUTINE TRSBOX or ALTMOV. Usually XBASE+XNEW is the<a name="line.357"></a>
<FONT color="green">358</FONT>         *       vector of variables for the next call of CALFUN. XNEW also satisfies<a name="line.358"></a>
<FONT color="green">359</FONT>         *       the SL and SU constraints in the way that has just been mentioned.<a name="line.359"></a>
<FONT color="green">360</FONT>         *     XALT is an alternative to XNEW, chosen by ALTMOV, that may replace XNEW<a name="line.360"></a>
<FONT color="green">361</FONT>         *       in order to increase the denominator in the updating of UPDATE.<a name="line.361"></a>
<FONT color="green">362</FONT>         *     D is reserved for a trial step from XOPT, which is usually XNEW-XOPT.<a name="line.362"></a>
<FONT color="green">363</FONT>         *     VLAG contains the values of the Lagrange functions at a new point X.<a name="line.363"></a>
<FONT color="green">364</FONT>         *       They are part of a product that requires VLAG to be of length NDIM.<a name="line.364"></a>
<FONT color="green">365</FONT>         *     W is a one-dimensional array that is used for working space. Its length<a name="line.365"></a>
<FONT color="green">366</FONT>         *       must be at least 3*NDIM = 3*(NPT+N).<a name="line.366"></a>
<FONT color="green">367</FONT>         *<a name="line.367"></a>
<FONT color="green">368</FONT>         * @param lowerBound Lower bounds.<a name="line.368"></a>
<FONT color="green">369</FONT>         * @param upperBound Upper bounds.<a name="line.369"></a>
<FONT color="green">370</FONT>         * @return the value of the objective at the optimum.<a name="line.370"></a>
<FONT color="green">371</FONT>         */<a name="line.371"></a>
<FONT color="green">372</FONT>        private double bobyqb(double[] lowerBound,<a name="line.372"></a>
<FONT color="green">373</FONT>                              double[] upperBound) {<a name="line.373"></a>
<FONT color="green">374</FONT>            printMethod(); // XXX<a name="line.374"></a>
<FONT color="green">375</FONT>    <a name="line.375"></a>
<FONT color="green">376</FONT>            final int n = currentBest.getDimension();<a name="line.376"></a>
<FONT color="green">377</FONT>            final int npt = numberOfInterpolationPoints;<a name="line.377"></a>
<FONT color="green">378</FONT>            final int np = n + 1;<a name="line.378"></a>
<FONT color="green">379</FONT>            final int nptm = npt - np;<a name="line.379"></a>
<FONT color="green">380</FONT>            final int nh = n * np / 2;<a name="line.380"></a>
<FONT color="green">381</FONT>    <a name="line.381"></a>
<FONT color="green">382</FONT>            final ArrayRealVector work1 = new ArrayRealVector(n);<a name="line.382"></a>
<FONT color="green">383</FONT>            final ArrayRealVector work2 = new ArrayRealVector(npt);<a name="line.383"></a>
<FONT color="green">384</FONT>            final ArrayRealVector work3 = new ArrayRealVector(npt);<a name="line.384"></a>
<FONT color="green">385</FONT>    <a name="line.385"></a>
<FONT color="green">386</FONT>            double cauchy = Double.NaN;<a name="line.386"></a>
<FONT color="green">387</FONT>            double alpha = Double.NaN;<a name="line.387"></a>
<FONT color="green">388</FONT>            double dsq = Double.NaN;<a name="line.388"></a>
<FONT color="green">389</FONT>            double crvmin = Double.NaN;<a name="line.389"></a>
<FONT color="green">390</FONT>    <a name="line.390"></a>
<FONT color="green">391</FONT>            // Set some constants.<a name="line.391"></a>
<FONT color="green">392</FONT>            // Parameter adjustments<a name="line.392"></a>
<FONT color="green">393</FONT>    <a name="line.393"></a>
<FONT color="green">394</FONT>            // Function Body<a name="line.394"></a>
<FONT color="green">395</FONT>    <a name="line.395"></a>
<FONT color="green">396</FONT>            // The call of PRELIM sets the elements of XBASE, XPT, FVAL, GOPT, HQ, PQ,<a name="line.396"></a>
<FONT color="green">397</FONT>            // BMAT and ZMAT for the first iteration, with the corresponding values of<a name="line.397"></a>
<FONT color="green">398</FONT>            // of NF and KOPT, which are the number of calls of CALFUN so far and the<a name="line.398"></a>
<FONT color="green">399</FONT>            // index of the interpolation point at the trust region centre. Then the<a name="line.399"></a>
<FONT color="green">400</FONT>            // initial XOPT is set too. The branch to label 720 occurs if MAXFUN is<a name="line.400"></a>
<FONT color="green">401</FONT>            // less than NPT. GOPT will be updated if KOPT is different from KBASE.<a name="line.401"></a>
<FONT color="green">402</FONT>    <a name="line.402"></a>
<FONT color="green">403</FONT>            trustRegionCenterInterpolationPointIndex = 0;<a name="line.403"></a>
<FONT color="green">404</FONT>    <a name="line.404"></a>
<FONT color="green">405</FONT>            prelim(lowerBound, upperBound);<a name="line.405"></a>
<FONT color="green">406</FONT>            double xoptsq = ZERO;<a name="line.406"></a>
<FONT color="green">407</FONT>            for (int i = 0; i &lt; n; i++) {<a name="line.407"></a>
<FONT color="green">408</FONT>                trustRegionCenterOffset.setEntry(i, interpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex, i));<a name="line.408"></a>
<FONT color="green">409</FONT>                // Computing 2nd power<a name="line.409"></a>
<FONT color="green">410</FONT>                final double deltaOne = trustRegionCenterOffset.getEntry(i);<a name="line.410"></a>
<FONT color="green">411</FONT>                xoptsq += deltaOne * deltaOne;<a name="line.411"></a>
<FONT color="green">412</FONT>            }<a name="line.412"></a>
<FONT color="green">413</FONT>            double fsave = fAtInterpolationPoints.getEntry(0);<a name="line.413"></a>
<FONT color="green">414</FONT>            final int kbase = 0;<a name="line.414"></a>
<FONT color="green">415</FONT>    <a name="line.415"></a>
<FONT color="green">416</FONT>            // Complete the settings that are required for the iterative procedure.<a name="line.416"></a>
<FONT color="green">417</FONT>    <a name="line.417"></a>
<FONT color="green">418</FONT>            int ntrits = 0;<a name="line.418"></a>
<FONT color="green">419</FONT>            int itest = 0;<a name="line.419"></a>
<FONT color="green">420</FONT>            int knew = 0;<a name="line.420"></a>
<FONT color="green">421</FONT>            int nfsav = getEvaluations();<a name="line.421"></a>
<FONT color="green">422</FONT>            double rho = initialTrustRegionRadius;<a name="line.422"></a>
<FONT color="green">423</FONT>            double delta = rho;<a name="line.423"></a>
<FONT color="green">424</FONT>            double diffa = ZERO;<a name="line.424"></a>
<FONT color="green">425</FONT>            double diffb = ZERO;<a name="line.425"></a>
<FONT color="green">426</FONT>            double diffc = ZERO;<a name="line.426"></a>
<FONT color="green">427</FONT>            double f = ZERO;<a name="line.427"></a>
<FONT color="green">428</FONT>            double beta = ZERO;<a name="line.428"></a>
<FONT color="green">429</FONT>            double adelt = ZERO;<a name="line.429"></a>
<FONT color="green">430</FONT>            double denom = ZERO;<a name="line.430"></a>
<FONT color="green">431</FONT>            double ratio = ZERO;<a name="line.431"></a>
<FONT color="green">432</FONT>            double dnorm = ZERO;<a name="line.432"></a>
<FONT color="green">433</FONT>            double scaden = ZERO;<a name="line.433"></a>
<FONT color="green">434</FONT>            double biglsq = ZERO;<a name="line.434"></a>
<FONT color="green">435</FONT>            double distsq = ZERO;<a name="line.435"></a>
<FONT color="green">436</FONT>    <a name="line.436"></a>
<FONT color="green">437</FONT>            // Update GOPT if necessary before the first iteration and after each<a name="line.437"></a>
<FONT color="green">438</FONT>            // call of RESCUE that makes a call of CALFUN.<a name="line.438"></a>
<FONT color="green">439</FONT>    <a name="line.439"></a>
<FONT color="green">440</FONT>            int state = 20;<a name="line.440"></a>
<FONT color="green">441</FONT>            for(;;) switch (state) {<a name="line.441"></a>
<FONT color="green">442</FONT>            case 20: {<a name="line.442"></a>
<FONT color="green">443</FONT>                printState(20); // XXX<a name="line.443"></a>
<FONT color="green">444</FONT>                if (trustRegionCenterInterpolationPointIndex != kbase) {<a name="line.444"></a>
<FONT color="green">445</FONT>                    int ih = 0;<a name="line.445"></a>
<FONT color="green">446</FONT>                    for (int j = 0; j &lt; n; j++) {<a name="line.446"></a>
<FONT color="green">447</FONT>                        for (int i = 0; i &lt;= j; i++) {<a name="line.447"></a>
<FONT color="green">448</FONT>                            if (i &lt; j) {<a name="line.448"></a>
<FONT color="green">449</FONT>                                gradientAtTrustRegionCenter.setEntry(j, gradientAtTrustRegionCenter.getEntry(j) + modelSecondDerivativesValues.getEntry(ih) * trustRegionCenterOffset.getEntry(i));<a name="line.449"></a>
<FONT color="green">450</FONT>                            }<a name="line.450"></a>
<FONT color="green">451</FONT>                            gradientAtTrustRegionCenter.setEntry(i, gradientAtTrustRegionCenter.getEntry(i) + modelSecondDerivativesValues.getEntry(ih) * trustRegionCenterOffset.getEntry(j));<a name="line.451"></a>
<FONT color="green">452</FONT>                            ih++;<a name="line.452"></a>
<FONT color="green">453</FONT>                        }<a name="line.453"></a>
<FONT color="green">454</FONT>                    }<a name="line.454"></a>
<FONT color="green">455</FONT>                    if (getEvaluations() &gt; npt) {<a name="line.455"></a>
<FONT color="green">456</FONT>                        for (int k = 0; k &lt; npt; k++) {<a name="line.456"></a>
<FONT color="green">457</FONT>                            double temp = ZERO;<a name="line.457"></a>
<FONT color="green">458</FONT>                            for (int j = 0; j &lt; n; j++) {<a name="line.458"></a>
<FONT color="green">459</FONT>                                temp += interpolationPoints.getEntry(k, j) * trustRegionCenterOffset.getEntry(j);<a name="line.459"></a>
<FONT color="green">460</FONT>                            }<a name="line.460"></a>
<FONT color="green">461</FONT>                            temp *= modelSecondDerivativesParameters.getEntry(k);<a name="line.461"></a>
<FONT color="green">462</FONT>                            for (int i = 0; i &lt; n; i++) {<a name="line.462"></a>
<FONT color="green">463</FONT>                                gradientAtTrustRegionCenter.setEntry(i, gradientAtTrustRegionCenter.getEntry(i) + temp * interpolationPoints.getEntry(k, i));<a name="line.463"></a>
<FONT color="green">464</FONT>                            }<a name="line.464"></a>
<FONT color="green">465</FONT>                        }<a name="line.465"></a>
<FONT color="green">466</FONT>                        // throw new PathIsExploredException(); // XXX<a name="line.466"></a>
<FONT color="green">467</FONT>                    }<a name="line.467"></a>
<FONT color="green">468</FONT>                }<a name="line.468"></a>
<FONT color="green">469</FONT>    <a name="line.469"></a>
<FONT color="green">470</FONT>                // Generate the next point in the trust region that provides a small value<a name="line.470"></a>
<FONT color="green">471</FONT>                // of the quadratic model subject to the constraints on the variables.<a name="line.471"></a>
<FONT color="green">472</FONT>                // The int NTRITS is set to the number "trust region" iterations that<a name="line.472"></a>
<FONT color="green">473</FONT>                // have occurred since the last "alternative" iteration. If the length<a name="line.473"></a>
<FONT color="green">474</FONT>                // of XNEW-XOPT is less than HALF*RHO, however, then there is a branch to<a name="line.474"></a>
<FONT color="green">475</FONT>                // label 650 or 680 with NTRITS=-1, instead of calculating F at XNEW.<a name="line.475"></a>
<FONT color="green">476</FONT>    <a name="line.476"></a>
<FONT color="green">477</FONT>            }<a name="line.477"></a>
<FONT color="green">478</FONT>            case 60: {<a name="line.478"></a>
<FONT color="green">479</FONT>                printState(60); // XXX<a name="line.479"></a>
<FONT color="green">480</FONT>                final ArrayRealVector gnew = new ArrayRealVector(n);<a name="line.480"></a>
<FONT color="green">481</FONT>                final ArrayRealVector xbdi = new ArrayRealVector(n);<a name="line.481"></a>
<FONT color="green">482</FONT>                final ArrayRealVector s = new ArrayRealVector(n);<a name="line.482"></a>
<FONT color="green">483</FONT>                final ArrayRealVector hs = new ArrayRealVector(n);<a name="line.483"></a>
<FONT color="green">484</FONT>                final ArrayRealVector hred = new ArrayRealVector(n);<a name="line.484"></a>
<FONT color="green">485</FONT>    <a name="line.485"></a>
<FONT color="green">486</FONT>                final double[] dsqCrvmin = trsbox(delta, gnew, xbdi, s,<a name="line.486"></a>
<FONT color="green">487</FONT>                                                  hs, hred);<a name="line.487"></a>
<FONT color="green">488</FONT>                dsq = dsqCrvmin[0];<a name="line.488"></a>
<FONT color="green">489</FONT>                crvmin = dsqCrvmin[1];<a name="line.489"></a>
<FONT color="green">490</FONT>    <a name="line.490"></a>
<FONT color="green">491</FONT>                // Computing MIN<a name="line.491"></a>
<FONT color="green">492</FONT>                double deltaOne = delta;<a name="line.492"></a>
<FONT color="green">493</FONT>                double deltaTwo = Math.sqrt(dsq);<a name="line.493"></a>
<FONT color="green">494</FONT>                dnorm = Math.min(deltaOne, deltaTwo);<a name="line.494"></a>
<FONT color="green">495</FONT>                if (dnorm &lt; HALF * rho) {<a name="line.495"></a>
<FONT color="green">496</FONT>                    ntrits = -1;<a name="line.496"></a>
<FONT color="green">497</FONT>                    // Computing 2nd power<a name="line.497"></a>
<FONT color="green">498</FONT>                    deltaOne = TEN * rho;<a name="line.498"></a>
<FONT color="green">499</FONT>                    distsq = deltaOne * deltaOne;<a name="line.499"></a>
<FONT color="green">500</FONT>                    if (getEvaluations() &lt;= nfsav + 2) {<a name="line.500"></a>
<FONT color="green">501</FONT>                        state = 650; break;<a name="line.501"></a>
<FONT color="green">502</FONT>                    }<a name="line.502"></a>
<FONT color="green">503</FONT>    <a name="line.503"></a>
<FONT color="green">504</FONT>                    // The following choice between labels 650 and 680 depends on whether or<a name="line.504"></a>
<FONT color="green">505</FONT>                    // not our work with the current RHO seems to be complete. Either RHO is<a name="line.505"></a>
<FONT color="green">506</FONT>                    // decreased or termination occurs if the errors in the quadratic model at<a name="line.506"></a>
<FONT color="green">507</FONT>                    // the last three interpolation points compare favourably with predictions<a name="line.507"></a>
<FONT color="green">508</FONT>                    // of likely improvements to the model within distance HALF*RHO of XOPT.<a name="line.508"></a>
<FONT color="green">509</FONT>    <a name="line.509"></a>
<FONT color="green">510</FONT>                    // Computing MAX<a name="line.510"></a>
<FONT color="green">511</FONT>                    deltaOne = Math.max(diffa, diffb);<a name="line.511"></a>
<FONT color="green">512</FONT>                    final double errbig = Math.max(deltaOne, diffc);<a name="line.512"></a>
<FONT color="green">513</FONT>                    final double frhosq = rho * ONE_OVER_EIGHT * rho;<a name="line.513"></a>
<FONT color="green">514</FONT>                    if (crvmin &gt; ZERO &amp;&amp;<a name="line.514"></a>
<FONT color="green">515</FONT>                        errbig &gt; frhosq * crvmin) {<a name="line.515"></a>
<FONT color="green">516</FONT>                        state = 650; break;<a name="line.516"></a>
<FONT color="green">517</FONT>                    }<a name="line.517"></a>
<FONT color="green">518</FONT>                    final double bdtol = errbig / rho;<a name="line.518"></a>
<FONT color="green">519</FONT>                    for (int j = 0; j &lt; n; j++) {<a name="line.519"></a>
<FONT color="green">520</FONT>                        double bdtest = bdtol;<a name="line.520"></a>
<FONT color="green">521</FONT>                        if (newPoint.getEntry(j) == lowerDifference.getEntry(j)) {<a name="line.521"></a>
<FONT color="green">522</FONT>                            bdtest = work1.getEntry(j);<a name="line.522"></a>
<FONT color="green">523</FONT>                        }<a name="line.523"></a>
<FONT color="green">524</FONT>                        if (newPoint.getEntry(j) == upperDifference.getEntry(j)) {<a name="line.524"></a>
<FONT color="green">525</FONT>                            bdtest = -work1.getEntry(j);<a name="line.525"></a>
<FONT color="green">526</FONT>                        }<a name="line.526"></a>
<FONT color="green">527</FONT>                        if (bdtest &lt; bdtol) {<a name="line.527"></a>
<FONT color="green">528</FONT>                            double curv = modelSecondDerivativesValues.getEntry((j + j * j) / 2);<a name="line.528"></a>
<FONT color="green">529</FONT>                            for (int k = 0; k &lt; npt; k++) {<a name="line.529"></a>
<FONT color="green">530</FONT>                                // Computing 2nd power<a name="line.530"></a>
<FONT color="green">531</FONT>                                final double d1 = interpolationPoints.getEntry(k, j);<a name="line.531"></a>
<FONT color="green">532</FONT>                                curv += modelSecondDerivativesParameters.getEntry(k) * (d1 * d1);<a name="line.532"></a>
<FONT color="green">533</FONT>                            }<a name="line.533"></a>
<FONT color="green">534</FONT>                            bdtest += HALF * curv * rho;<a name="line.534"></a>
<FONT color="green">535</FONT>                            if (bdtest &lt; bdtol) {<a name="line.535"></a>
<FONT color="green">536</FONT>                                state = 650; break;<a name="line.536"></a>
<FONT color="green">537</FONT>                            }<a name="line.537"></a>
<FONT color="green">538</FONT>                            // throw new PathIsExploredException(); // XXX<a name="line.538"></a>
<FONT color="green">539</FONT>                        }<a name="line.539"></a>
<FONT color="green">540</FONT>                    }<a name="line.540"></a>
<FONT color="green">541</FONT>                    state = 680; break;<a name="line.541"></a>
<FONT color="green">542</FONT>                }<a name="line.542"></a>
<FONT color="green">543</FONT>                ++ntrits;<a name="line.543"></a>
<FONT color="green">544</FONT>    <a name="line.544"></a>
<FONT color="green">545</FONT>                // Severe cancellation is likely to occur if XOPT is too far from XBASE.<a name="line.545"></a>
<FONT color="green">546</FONT>                // If the following test holds, then XBASE is shifted so that XOPT becomes<a name="line.546"></a>
<FONT color="green">547</FONT>                // zero. The appropriate changes are made to BMAT and to the second<a name="line.547"></a>
<FONT color="green">548</FONT>                // derivatives of the current model, beginning with the changes to BMAT<a name="line.548"></a>
<FONT color="green">549</FONT>                // that do not depend on ZMAT. VLAG is used temporarily for working space.<a name="line.549"></a>
<FONT color="green">550</FONT>    <a name="line.550"></a>
<FONT color="green">551</FONT>            }<a name="line.551"></a>
<FONT color="green">552</FONT>            case 90: {<a name="line.552"></a>
<FONT color="green">553</FONT>                printState(90); // XXX<a name="line.553"></a>
<FONT color="green">554</FONT>                if (dsq &lt;= xoptsq * ONE_OVER_A_THOUSAND) {<a name="line.554"></a>
<FONT color="green">555</FONT>                    final double fracsq = xoptsq * ONE_OVER_FOUR;<a name="line.555"></a>
<FONT color="green">556</FONT>                    double sumpq = ZERO;<a name="line.556"></a>
<FONT color="green">557</FONT>                    // final RealVector sumVector<a name="line.557"></a>
<FONT color="green">558</FONT>                    //     = new ArrayRealVector(npt, -HALF * xoptsq).add(interpolationPoints.operate(trustRegionCenter));<a name="line.558"></a>
<FONT color="green">559</FONT>                    for (int k = 0; k &lt; npt; k++) {<a name="line.559"></a>
<FONT color="green">560</FONT>                        sumpq += modelSecondDerivativesParameters.getEntry(k);<a name="line.560"></a>
<FONT color="green">561</FONT>                        double sum = -HALF * xoptsq;<a name="line.561"></a>
<FONT color="green">562</FONT>                        for (int i = 0; i &lt; n; i++) {<a name="line.562"></a>
<FONT color="green">563</FONT>                            sum += interpolationPoints.getEntry(k, i) * trustRegionCenterOffset.getEntry(i);<a name="line.563"></a>
<FONT color="green">564</FONT>                        }<a name="line.564"></a>
<FONT color="green">565</FONT>                        // sum = sumVector.getEntry(k); // XXX "testAckley" and "testDiffPow" fail.<a name="line.565"></a>
<FONT color="green">566</FONT>                        work2.setEntry(k, sum);<a name="line.566"></a>
<FONT color="green">567</FONT>                        final double temp = fracsq - HALF * sum;<a name="line.567"></a>
<FONT color="green">568</FONT>                        for (int i = 0; i &lt; n; i++) {<a name="line.568"></a>
<FONT color="green">569</FONT>                            work1.setEntry(i, bMatrix.getEntry(k, i));<a name="line.569"></a>
<FONT color="green">570</FONT>                            lagrangeValuesAtNewPoint.setEntry(i, sum * interpolationPoints.getEntry(k, i) + temp * trustRegionCenterOffset.getEntry(i));<a name="line.570"></a>
<FONT color="green">571</FONT>                            final int ip = npt + i;<a name="line.571"></a>
<FONT color="green">572</FONT>                            for (int j = 0; j &lt;= i; j++) {<a name="line.572"></a>
<FONT color="green">573</FONT>                                bMatrix.setEntry(ip, j,<a name="line.573"></a>
<FONT color="green">574</FONT>                                              bMatrix.getEntry(ip, j)<a name="line.574"></a>
<FONT color="green">575</FONT>                                              + work1.getEntry(i) * lagrangeValuesAtNewPoint.getEntry(j)<a name="line.575"></a>
<FONT color="green">576</FONT>                                              + lagrangeValuesAtNewPoint.getEntry(i) * work1.getEntry(j));<a name="line.576"></a>
<FONT color="green">577</FONT>                            }<a name="line.577"></a>
<FONT color="green">578</FONT>                        }<a name="line.578"></a>
<FONT color="green">579</FONT>                    }<a name="line.579"></a>
<FONT color="green">580</FONT>    <a name="line.580"></a>
<FONT color="green">581</FONT>                    // Then the revisions of BMAT that depend on ZMAT are calculated.<a name="line.581"></a>
<FONT color="green">582</FONT>    <a name="line.582"></a>
<FONT color="green">583</FONT>                    for (int m = 0; m &lt; nptm; m++) {<a name="line.583"></a>
<FONT color="green">584</FONT>                        double sumz = ZERO;<a name="line.584"></a>
<FONT color="green">585</FONT>                        double sumw = ZERO;<a name="line.585"></a>
<FONT color="green">586</FONT>                        for (int k = 0; k &lt; npt; k++) {<a name="line.586"></a>
<FONT color="green">587</FONT>                            sumz += zMatrix.getEntry(k, m);<a name="line.587"></a>
<FONT color="green">588</FONT>                            lagrangeValuesAtNewPoint.setEntry(k, work2.getEntry(k) * zMatrix.getEntry(k, m));<a name="line.588"></a>
<FONT color="green">589</FONT>                            sumw += lagrangeValuesAtNewPoint.getEntry(k);<a name="line.589"></a>
<FONT color="green">590</FONT>                        }<a name="line.590"></a>
<FONT color="green">591</FONT>                        for (int j = 0; j &lt; n; j++) {<a name="line.591"></a>
<FONT color="green">592</FONT>                            double sum = (fracsq * sumz - HALF * sumw) * trustRegionCenterOffset.getEntry(j);<a name="line.592"></a>
<FONT color="green">593</FONT>                            for (int k = 0; k &lt; npt; k++) {<a name="line.593"></a>
<FONT color="green">594</FONT>                                sum += lagrangeValuesAtNewPoint.getEntry(k) * interpolationPoints.getEntry(k, j);<a name="line.594"></a>
<FONT color="green">595</FONT>                            }<a name="line.595"></a>
<FONT color="green">596</FONT>                            work1.setEntry(j, sum);<a name="line.596"></a>
<FONT color="green">597</FONT>                            for (int k = 0; k &lt; npt; k++) {<a name="line.597"></a>
<FONT color="green">598</FONT>                                bMatrix.setEntry(k, j,<a name="line.598"></a>
<FONT color="green">599</FONT>                                              bMatrix.getEntry(k, j)<a name="line.599"></a>
<FONT color="green">600</FONT>                                              + sum * zMatrix.getEntry(k, m));<a name="line.600"></a>
<FONT color="green">601</FONT>                            }<a name="line.601"></a>
<FONT color="green">602</FONT>                        }<a name="line.602"></a>
<FONT color="green">603</FONT>                        for (int i = 0; i &lt; n; i++) {<a name="line.603"></a>
<FONT color="green">604</FONT>                            final int ip = i + npt;<a name="line.604"></a>
<FONT color="green">605</FONT>                            final double temp = work1.getEntry(i);<a name="line.605"></a>
<FONT color="green">606</FONT>                            for (int j = 0; j &lt;= i; j++) {<a name="line.606"></a>
<FONT color="green">607</FONT>                                bMatrix.setEntry(ip, j,<a name="line.607"></a>
<FONT color="green">608</FONT>                                              bMatrix.getEntry(ip, j)<a name="line.608"></a>
<FONT color="green">609</FONT>                                              + temp * work1.getEntry(j));<a name="line.609"></a>
<FONT color="green">610</FONT>                            }<a name="line.610"></a>
<FONT color="green">611</FONT>                        }<a name="line.611"></a>
<FONT color="green">612</FONT>                    }<a name="line.612"></a>
<FONT color="green">613</FONT>    <a name="line.613"></a>
<FONT color="green">614</FONT>                    // The following instructions complete the shift, including the changes<a name="line.614"></a>
<FONT color="green">615</FONT>                    // to the second derivative parameters of the quadratic model.<a name="line.615"></a>
<FONT color="green">616</FONT>    <a name="line.616"></a>
<FONT color="green">617</FONT>                    int ih = 0;<a name="line.617"></a>
<FONT color="green">618</FONT>                    for (int j = 0; j &lt; n; j++) {<a name="line.618"></a>
<FONT color="green">619</FONT>                        work1.setEntry(j, -HALF * sumpq * trustRegionCenterOffset.getEntry(j));<a name="line.619"></a>
<FONT color="green">620</FONT>                        for (int k = 0; k &lt; npt; k++) {<a name="line.620"></a>
<FONT color="green">621</FONT>                            work1.setEntry(j, work1.getEntry(j) + modelSecondDerivativesParameters.getEntry(k) * interpolationPoints.getEntry(k, j));<a name="line.621"></a>
<FONT color="green">622</FONT>                            interpolationPoints.setEntry(k, j, interpolationPoints.getEntry(k, j) - trustRegionCenterOffset.getEntry(j));<a name="line.622"></a>
<FONT color="green">623</FONT>                        }<a name="line.623"></a>
<FONT color="green">624</FONT>                        for (int i = 0; i &lt;= j; i++) {<a name="line.624"></a>
<FONT color="green">625</FONT>                             modelSecondDerivativesValues.setEntry(ih,<a name="line.625"></a>
<FONT color="green">626</FONT>                                        modelSecondDerivativesValues.getEntry(ih)<a name="line.626"></a>
<FONT color="green">627</FONT>                                        + work1.getEntry(i) * trustRegionCenterOffset.getEntry(j)<a name="line.627"></a>
<FONT color="green">628</FONT>                                        + trustRegionCenterOffset.getEntry(i) * work1.getEntry(j));<a name="line.628"></a>
<FONT color="green">629</FONT>                            bMatrix.setEntry(npt + i, j, bMatrix.getEntry(npt + j, i));<a name="line.629"></a>
<FONT color="green">630</FONT>                            ih++;<a name="line.630"></a>
<FONT color="green">631</FONT>                        }<a name="line.631"></a>
<FONT color="green">632</FONT>                    }<a name="line.632"></a>
<FONT color="green">633</FONT>                    for (int i = 0; i &lt; n; i++) {<a name="line.633"></a>
<FONT color="green">634</FONT>                        originShift.setEntry(i, originShift.getEntry(i) + trustRegionCenterOffset.getEntry(i));<a name="line.634"></a>
<FONT color="green">635</FONT>                        newPoint.setEntry(i, newPoint.getEntry(i) - trustRegionCenterOffset.getEntry(i));<a name="line.635"></a>
<FONT color="green">636</FONT>                        lowerDifference.setEntry(i, lowerDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i));<a name="line.636"></a>
<FONT color="green">637</FONT>                        upperDifference.setEntry(i, upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i));<a name="line.637"></a>
<FONT color="green">638</FONT>                        trustRegionCenterOffset.setEntry(i, ZERO);<a name="line.638"></a>
<FONT color="green">639</FONT>                    }<a name="line.639"></a>
<FONT color="green">640</FONT>                    xoptsq = ZERO;<a name="line.640"></a>
<FONT color="green">641</FONT>                }<a name="line.641"></a>
<FONT color="green">642</FONT>                if (ntrits == 0) {<a name="line.642"></a>
<FONT color="green">643</FONT>                    state = 210; break;<a name="line.643"></a>
<FONT color="green">644</FONT>                }<a name="line.644"></a>
<FONT color="green">645</FONT>                state = 230; break;<a name="line.645"></a>
<FONT color="green">646</FONT>    <a name="line.646"></a>
<FONT color="green">647</FONT>                // XBASE is also moved to XOPT by a call of RESCUE. This calculation is<a name="line.647"></a>
<FONT color="green">648</FONT>                // more expensive than the previous shift, because new matrices BMAT and<a name="line.648"></a>
<FONT color="green">649</FONT>                // ZMAT are generated from scratch, which may include the replacement of<a name="line.649"></a>
<FONT color="green">650</FONT>                // interpolation points whose positions seem to be causing near linear<a name="line.650"></a>
<FONT color="green">651</FONT>                // dependence in the interpolation conditions. Therefore RESCUE is called<a name="line.651"></a>
<FONT color="green">652</FONT>                // only if rounding errors have reduced by at least a factor of two the<a name="line.652"></a>
<FONT color="green">653</FONT>                // denominator of the formula for updating the H matrix. It provides a<a name="line.653"></a>
<FONT color="green">654</FONT>                // useful safeguard, but is not invoked in most applications of BOBYQA.<a name="line.654"></a>
<FONT color="green">655</FONT>    <a name="line.655"></a>
<FONT color="green">656</FONT>            }<a name="line.656"></a>
<FONT color="green">657</FONT>            case 210: {<a name="line.657"></a>
<FONT color="green">658</FONT>                printState(210); // XXX<a name="line.658"></a>
<FONT color="green">659</FONT>                // Pick two alternative vectors of variables, relative to XBASE, that<a name="line.659"></a>
<FONT color="green">660</FONT>                // are suitable as new positions of the KNEW-th interpolation point.<a name="line.660"></a>
<FONT color="green">661</FONT>                // Firstly, XNEW is set to the point on a line through XOPT and another<a name="line.661"></a>
<FONT color="green">662</FONT>                // interpolation point that minimizes the predicted value of the next<a name="line.662"></a>
<FONT color="green">663</FONT>                // denominator, subject to ||XNEW - XOPT|| .LEQ. ADELT and to the SL<a name="line.663"></a>
<FONT color="green">664</FONT>                // and SU bounds. Secondly, XALT is set to the best feasible point on<a name="line.664"></a>
<FONT color="green">665</FONT>                // a constrained version of the Cauchy step of the KNEW-th Lagrange<a name="line.665"></a>
<FONT color="green">666</FONT>                // function, the corresponding value of the square of this function<a name="line.666"></a>
<FONT color="green">667</FONT>                // being returned in CAUCHY. The choice between these alternatives is<a name="line.667"></a>
<FONT color="green">668</FONT>                // going to be made when the denominator is calculated.<a name="line.668"></a>
<FONT color="green">669</FONT>    <a name="line.669"></a>
<FONT color="green">670</FONT>                final double[] alphaCauchy = altmov(knew, adelt);<a name="line.670"></a>
<FONT color="green">671</FONT>                alpha = alphaCauchy[0];<a name="line.671"></a>
<FONT color="green">672</FONT>                cauchy = alphaCauchy[1];<a name="line.672"></a>
<FONT color="green">673</FONT>    <a name="line.673"></a>
<FONT color="green">674</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.674"></a>
<FONT color="green">675</FONT>                    trialStepPoint.setEntry(i, newPoint.getEntry(i) - trustRegionCenterOffset.getEntry(i));<a name="line.675"></a>
<FONT color="green">676</FONT>                }<a name="line.676"></a>
<FONT color="green">677</FONT>    <a name="line.677"></a>
<FONT color="green">678</FONT>                // Calculate VLAG and BETA for the current choice of D. The scalar<a name="line.678"></a>
<FONT color="green">679</FONT>                // product of D with XPT(K,.) is going to be held in W(NPT+K) for<a name="line.679"></a>
<FONT color="green">680</FONT>                // use when VQUAD is calculated.<a name="line.680"></a>
<FONT color="green">681</FONT>    <a name="line.681"></a>
<FONT color="green">682</FONT>            }<a name="line.682"></a>
<FONT color="green">683</FONT>            case 230: {<a name="line.683"></a>
<FONT color="green">684</FONT>                printState(230); // XXX<a name="line.684"></a>
<FONT color="green">685</FONT>                for (int k = 0; k &lt; npt; k++) {<a name="line.685"></a>
<FONT color="green">686</FONT>                    double suma = ZERO;<a name="line.686"></a>
<FONT color="green">687</FONT>                    double sumb = ZERO;<a name="line.687"></a>
<FONT color="green">688</FONT>                    double sum = ZERO;<a name="line.688"></a>
<FONT color="green">689</FONT>                    for (int j = 0; j &lt; n; j++) {<a name="line.689"></a>
<FONT color="green">690</FONT>                        suma += interpolationPoints.getEntry(k, j) * trialStepPoint.getEntry(j);<a name="line.690"></a>
<FONT color="green">691</FONT>                        sumb += interpolationPoints.getEntry(k, j) * trustRegionCenterOffset.getEntry(j);<a name="line.691"></a>
<FONT color="green">692</FONT>                        sum += bMatrix.getEntry(k, j) * trialStepPoint.getEntry(j);<a name="line.692"></a>
<FONT color="green">693</FONT>                    }<a name="line.693"></a>
<FONT color="green">694</FONT>                    work3.setEntry(k, suma * (HALF * suma + sumb));<a name="line.694"></a>
<FONT color="green">695</FONT>                    lagrangeValuesAtNewPoint.setEntry(k, sum);<a name="line.695"></a>
<FONT color="green">696</FONT>                    work2.setEntry(k, suma);<a name="line.696"></a>
<FONT color="green">697</FONT>                }<a name="line.697"></a>
<FONT color="green">698</FONT>                beta = ZERO;<a name="line.698"></a>
<FONT color="green">699</FONT>                for (int m = 0; m &lt; nptm; m++) {<a name="line.699"></a>
<FONT color="green">700</FONT>                    double sum = ZERO;<a name="line.700"></a>
<FONT color="green">701</FONT>                    for (int k = 0; k &lt; npt; k++) {<a name="line.701"></a>
<FONT color="green">702</FONT>                        sum += zMatrix.getEntry(k, m) * work3.getEntry(k);<a name="line.702"></a>
<FONT color="green">703</FONT>                    }<a name="line.703"></a>
<FONT color="green">704</FONT>                    beta -= sum * sum;<a name="line.704"></a>
<FONT color="green">705</FONT>                    for (int k = 0; k &lt; npt; k++) {<a name="line.705"></a>
<FONT color="green">706</FONT>                        lagrangeValuesAtNewPoint.setEntry(k, lagrangeValuesAtNewPoint.getEntry(k) + sum * zMatrix.getEntry(k, m));<a name="line.706"></a>
<FONT color="green">707</FONT>                    }<a name="line.707"></a>
<FONT color="green">708</FONT>                }<a name="line.708"></a>
<FONT color="green">709</FONT>                dsq = ZERO;<a name="line.709"></a>
<FONT color="green">710</FONT>                double bsum = ZERO;<a name="line.710"></a>
<FONT color="green">711</FONT>                double dx = ZERO;<a name="line.711"></a>
<FONT color="green">712</FONT>                for (int j = 0; j &lt; n; j++) {<a name="line.712"></a>
<FONT color="green">713</FONT>                    // Computing 2nd power<a name="line.713"></a>
<FONT color="green">714</FONT>                    final double d1 = trialStepPoint.getEntry(j);<a name="line.714"></a>
<FONT color="green">715</FONT>                    dsq += d1 * d1;<a name="line.715"></a>
<FONT color="green">716</FONT>                    double sum = ZERO;<a name="line.716"></a>
<FONT color="green">717</FONT>                    for (int k = 0; k &lt; npt; k++) {<a name="line.717"></a>
<FONT color="green">718</FONT>                        sum += work3.getEntry(k) * bMatrix.getEntry(k, j);<a name="line.718"></a>
<FONT color="green">719</FONT>                    }<a name="line.719"></a>
<FONT color="green">720</FONT>                    bsum += sum * trialStepPoint.getEntry(j);<a name="line.720"></a>
<FONT color="green">721</FONT>                    final int jp = npt + j;<a name="line.721"></a>
<FONT color="green">722</FONT>                    for (int i = 0; i &lt; n; i++) {<a name="line.722"></a>
<FONT color="green">723</FONT>                        sum += bMatrix.getEntry(jp, i) * trialStepPoint.getEntry(i);<a name="line.723"></a>
<FONT color="green">724</FONT>                    }<a name="line.724"></a>
<FONT color="green">725</FONT>                    lagrangeValuesAtNewPoint.setEntry(jp, sum);<a name="line.725"></a>
<FONT color="green">726</FONT>                    bsum += sum * trialStepPoint.getEntry(j);<a name="line.726"></a>
<FONT color="green">727</FONT>                    dx += trialStepPoint.getEntry(j) * trustRegionCenterOffset.getEntry(j);<a name="line.727"></a>
<FONT color="green">728</FONT>                }<a name="line.728"></a>
<FONT color="green">729</FONT>    <a name="line.729"></a>
<FONT color="green">730</FONT>                beta = dx * dx + dsq * (xoptsq + dx + dx + HALF * dsq) + beta - bsum; // Original<a name="line.730"></a>
<FONT color="green">731</FONT>                // beta += dx * dx + dsq * (xoptsq + dx + dx + HALF * dsq) - bsum; // XXX "testAckley" and "testDiffPow" fail.<a name="line.731"></a>
<FONT color="green">732</FONT>                // beta = dx * dx + dsq * (xoptsq + 2 * dx + HALF * dsq) + beta - bsum; // XXX "testDiffPow" fails.<a name="line.732"></a>
<FONT color="green">733</FONT>    <a name="line.733"></a>
<FONT color="green">734</FONT>                lagrangeValuesAtNewPoint.setEntry(trustRegionCenterInterpolationPointIndex,<a name="line.734"></a>
<FONT color="green">735</FONT>                              lagrangeValuesAtNewPoint.getEntry(trustRegionCenterInterpolationPointIndex) + ONE);<a name="line.735"></a>
<FONT color="green">736</FONT>    <a name="line.736"></a>
<FONT color="green">737</FONT>                // If NTRITS is zero, the denominator may be increased by replacing<a name="line.737"></a>
<FONT color="green">738</FONT>                // the step D of ALTMOV by a Cauchy step. Then RESCUE may be called if<a name="line.738"></a>
<FONT color="green">739</FONT>                // rounding errors have damaged the chosen denominator.<a name="line.739"></a>
<FONT color="green">740</FONT>    <a name="line.740"></a>
<FONT color="green">741</FONT>                if (ntrits == 0) {<a name="line.741"></a>
<FONT color="green">742</FONT>                    // Computing 2nd power<a name="line.742"></a>
<FONT color="green">743</FONT>                    final double d1 = lagrangeValuesAtNewPoint.getEntry(knew);<a name="line.743"></a>
<FONT color="green">744</FONT>                    denom = d1 * d1 + alpha * beta;<a name="line.744"></a>
<FONT color="green">745</FONT>                    if (denom &lt; cauchy &amp;&amp; cauchy &gt; ZERO) {<a name="line.745"></a>
<FONT color="green">746</FONT>                        for (int i = 0; i &lt; n; i++) {<a name="line.746"></a>
<FONT color="green">747</FONT>                            newPoint.setEntry(i, alternativeNewPoint.getEntry(i));<a name="line.747"></a>
<FONT color="green">748</FONT>                            trialStepPoint.setEntry(i, newPoint.getEntry(i) - trustRegionCenterOffset.getEntry(i));<a name="line.748"></a>
<FONT color="green">749</FONT>                        }<a name="line.749"></a>
<FONT color="green">750</FONT>                        cauchy = ZERO; // XXX Useful statement?<a name="line.750"></a>
<FONT color="green">751</FONT>                        state = 230; break;<a name="line.751"></a>
<FONT color="green">752</FONT>                    }<a name="line.752"></a>
<FONT color="green">753</FONT>                    // Alternatively, if NTRITS is positive, then set KNEW to the index of<a name="line.753"></a>
<FONT color="green">754</FONT>                    // the next interpolation point to be deleted to make room for a trust<a name="line.754"></a>
<FONT color="green">755</FONT>                    // region step. Again RESCUE may be called if rounding errors have damaged_<a name="line.755"></a>
<FONT color="green">756</FONT>                    // the chosen denominator, which is the reason for attempting to select<a name="line.756"></a>
<FONT color="green">757</FONT>                    // KNEW before calculating the next value of the objective function.<a name="line.757"></a>
<FONT color="green">758</FONT>    <a name="line.758"></a>
<FONT color="green">759</FONT>                } else {<a name="line.759"></a>
<FONT color="green">760</FONT>                    final double delsq = delta * delta;<a name="line.760"></a>
<FONT color="green">761</FONT>                    scaden = ZERO;<a name="line.761"></a>
<FONT color="green">762</FONT>                    biglsq = ZERO;<a name="line.762"></a>
<FONT color="green">763</FONT>                    knew = 0;<a name="line.763"></a>
<FONT color="green">764</FONT>                    for (int k = 0; k &lt; npt; k++) {<a name="line.764"></a>
<FONT color="green">765</FONT>                        if (k == trustRegionCenterInterpolationPointIndex) {<a name="line.765"></a>
<FONT color="green">766</FONT>                            continue;<a name="line.766"></a>
<FONT color="green">767</FONT>                        }<a name="line.767"></a>
<FONT color="green">768</FONT>                        double hdiag = ZERO;<a name="line.768"></a>
<FONT color="green">769</FONT>                        for (int m = 0; m &lt; nptm; m++) {<a name="line.769"></a>
<FONT color="green">770</FONT>                            // Computing 2nd power<a name="line.770"></a>
<FONT color="green">771</FONT>                            final double d1 = zMatrix.getEntry(k, m);<a name="line.771"></a>
<FONT color="green">772</FONT>                            hdiag += d1 * d1;<a name="line.772"></a>
<FONT color="green">773</FONT>                        }<a name="line.773"></a>
<FONT color="green">774</FONT>                        // Computing 2nd power<a name="line.774"></a>
<FONT color="green">775</FONT>                        final double d2 = lagrangeValuesAtNewPoint.getEntry(k);<a name="line.775"></a>
<FONT color="green">776</FONT>                        final double den = beta * hdiag + d2 * d2;<a name="line.776"></a>
<FONT color="green">777</FONT>                        distsq = ZERO;<a name="line.777"></a>
<FONT color="green">778</FONT>                        for (int j = 0; j &lt; n; j++) {<a name="line.778"></a>
<FONT color="green">779</FONT>                            // Computing 2nd power<a name="line.779"></a>
<FONT color="green">780</FONT>                            final double d3 = interpolationPoints.getEntry(k, j) - trustRegionCenterOffset.getEntry(j);<a name="line.780"></a>
<FONT color="green">781</FONT>                            distsq += d3 * d3;<a name="line.781"></a>
<FONT color="green">782</FONT>                        }<a name="line.782"></a>
<FONT color="green">783</FONT>                        // Computing MAX<a name="line.783"></a>
<FONT color="green">784</FONT>                        // Computing 2nd power<a name="line.784"></a>
<FONT color="green">785</FONT>                        final double d4 = distsq / delsq;<a name="line.785"></a>
<FONT color="green">786</FONT>                        final double temp = Math.max(ONE, d4 * d4);<a name="line.786"></a>
<FONT color="green">787</FONT>                        if (temp * den &gt; scaden) {<a name="line.787"></a>
<FONT color="green">788</FONT>                            scaden = temp * den;<a name="line.788"></a>
<FONT color="green">789</FONT>                            knew = k;<a name="line.789"></a>
<FONT color="green">790</FONT>                            denom = den;<a name="line.790"></a>
<FONT color="green">791</FONT>                        }<a name="line.791"></a>
<FONT color="green">792</FONT>                        // Computing MAX<a name="line.792"></a>
<FONT color="green">793</FONT>                        // Computing 2nd power<a name="line.793"></a>
<FONT color="green">794</FONT>                        final double d5 = lagrangeValuesAtNewPoint.getEntry(k);<a name="line.794"></a>
<FONT color="green">795</FONT>                        biglsq = Math.max(biglsq, temp * (d5 * d5));<a name="line.795"></a>
<FONT color="green">796</FONT>                    }<a name="line.796"></a>
<FONT color="green">797</FONT>                }<a name="line.797"></a>
<FONT color="green">798</FONT>    <a name="line.798"></a>
<FONT color="green">799</FONT>                // Put the variables for the next calculation of the objective function<a name="line.799"></a>
<FONT color="green">800</FONT>                //   in XNEW, with any adjustments for the bounds.<a name="line.800"></a>
<FONT color="green">801</FONT>    <a name="line.801"></a>
<FONT color="green">802</FONT>                // Calculate the value of the objective function at XBASE+XNEW, unless<a name="line.802"></a>
<FONT color="green">803</FONT>                //   the limit on the number of calculations of F has been reached.<a name="line.803"></a>
<FONT color="green">804</FONT>    <a name="line.804"></a>
<FONT color="green">805</FONT>            }<a name="line.805"></a>
<FONT color="green">806</FONT>            case 360: {<a name="line.806"></a>
<FONT color="green">807</FONT>                printState(360); // XXX<a name="line.807"></a>
<FONT color="green">808</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.808"></a>
<FONT color="green">809</FONT>                    // Computing MIN<a name="line.809"></a>
<FONT color="green">810</FONT>                    // Computing MAX<a name="line.810"></a>
<FONT color="green">811</FONT>                    final double d3 = lowerBound[i];<a name="line.811"></a>
<FONT color="green">812</FONT>                    final double d4 = originShift.getEntry(i) + newPoint.getEntry(i);<a name="line.812"></a>
<FONT color="green">813</FONT>                    final double d1 = Math.max(d3, d4);<a name="line.813"></a>
<FONT color="green">814</FONT>                    final double d2 = upperBound[i];<a name="line.814"></a>
<FONT color="green">815</FONT>                    currentBest.setEntry(i, Math.min(d1, d2));<a name="line.815"></a>
<FONT color="green">816</FONT>                    if (newPoint.getEntry(i) == lowerDifference.getEntry(i)) {<a name="line.816"></a>
<FONT color="green">817</FONT>                        currentBest.setEntry(i, lowerBound[i]);<a name="line.817"></a>
<FONT color="green">818</FONT>                    }<a name="line.818"></a>
<FONT color="green">819</FONT>                    if (newPoint.getEntry(i) == upperDifference.getEntry(i)) {<a name="line.819"></a>
<FONT color="green">820</FONT>                        currentBest.setEntry(i, upperBound[i]);<a name="line.820"></a>
<FONT color="green">821</FONT>                    }<a name="line.821"></a>
<FONT color="green">822</FONT>                }<a name="line.822"></a>
<FONT color="green">823</FONT>    <a name="line.823"></a>
<FONT color="green">824</FONT>                f = computeObjectiveValue(currentBest.toArray());<a name="line.824"></a>
<FONT color="green">825</FONT>    <a name="line.825"></a>
<FONT color="green">826</FONT>                if (!isMinimize)<a name="line.826"></a>
<FONT color="green">827</FONT>                    f = -f;<a name="line.827"></a>
<FONT color="green">828</FONT>                if (ntrits == -1) {<a name="line.828"></a>
<FONT color="green">829</FONT>                    fsave = f;<a name="line.829"></a>
<FONT color="green">830</FONT>                    state = 720; break;<a name="line.830"></a>
<FONT color="green">831</FONT>                }<a name="line.831"></a>
<FONT color="green">832</FONT>    <a name="line.832"></a>
<FONT color="green">833</FONT>                // Use the quadratic model to predict the change in F due to the step D,<a name="line.833"></a>
<FONT color="green">834</FONT>                //   and set DIFF to the error of this prediction.<a name="line.834"></a>
<FONT color="green">835</FONT>    <a name="line.835"></a>
<FONT color="green">836</FONT>                final double fopt = fAtInterpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex);<a name="line.836"></a>
<FONT color="green">837</FONT>                double vquad = ZERO;<a name="line.837"></a>
<FONT color="green">838</FONT>                int ih = 0;<a name="line.838"></a>
<FONT color="green">839</FONT>                for (int j = 0; j &lt; n; j++) {<a name="line.839"></a>
<FONT color="green">840</FONT>                    vquad += trialStepPoint.getEntry(j) * gradientAtTrustRegionCenter.getEntry(j);<a name="line.840"></a>
<FONT color="green">841</FONT>                    for (int i = 0; i &lt;= j; i++) {<a name="line.841"></a>
<FONT color="green">842</FONT>                        double temp = trialStepPoint.getEntry(i) * trialStepPoint.getEntry(j);<a name="line.842"></a>
<FONT color="green">843</FONT>                        if (i == j) {<a name="line.843"></a>
<FONT color="green">844</FONT>                            temp *= HALF;<a name="line.844"></a>
<FONT color="green">845</FONT>                        }<a name="line.845"></a>
<FONT color="green">846</FONT>                        vquad += modelSecondDerivativesValues.getEntry(ih) * temp;<a name="line.846"></a>
<FONT color="green">847</FONT>                        ih++;<a name="line.847"></a>
<FONT color="green">848</FONT>                   }<a name="line.848"></a>
<FONT color="green">849</FONT>                }<a name="line.849"></a>
<FONT color="green">850</FONT>                for (int k = 0; k &lt; npt; k++) {<a name="line.850"></a>
<FONT color="green">851</FONT>                    // Computing 2nd power<a name="line.851"></a>
<FONT color="green">852</FONT>                    final double d1 = work2.getEntry(k);<a name="line.852"></a>
<FONT color="green">853</FONT>                    final double d2 = d1 * d1; // "d1" must be squared first to prevent test failures.<a name="line.853"></a>
<FONT color="green">854</FONT>                    vquad += HALF * modelSecondDerivativesParameters.getEntry(k) * d2;<a name="line.854"></a>
<FONT color="green">855</FONT>                }<a name="line.855"></a>
<FONT color="green">856</FONT>                final double diff = f - fopt - vquad;<a name="line.856"></a>
<FONT color="green">857</FONT>                diffc = diffb;<a name="line.857"></a>
<FONT color="green">858</FONT>                diffb = diffa;<a name="line.858"></a>
<FONT color="green">859</FONT>                diffa = Math.abs(diff);<a name="line.859"></a>
<FONT color="green">860</FONT>                if (dnorm &gt; rho) {<a name="line.860"></a>
<FONT color="green">861</FONT>                    nfsav = getEvaluations();<a name="line.861"></a>
<FONT color="green">862</FONT>                }<a name="line.862"></a>
<FONT color="green">863</FONT>    <a name="line.863"></a>
<FONT color="green">864</FONT>                // Pick the next value of DELTA after a trust region step.<a name="line.864"></a>
<FONT color="green">865</FONT>    <a name="line.865"></a>
<FONT color="green">866</FONT>                if (ntrits &gt; 0) {<a name="line.866"></a>
<FONT color="green">867</FONT>                    if (vquad &gt;= ZERO) {<a name="line.867"></a>
<FONT color="green">868</FONT>                        throw new MathIllegalStateException(LocalizedFormats.TRUST_REGION_STEP_FAILED, vquad);<a name="line.868"></a>
<FONT color="green">869</FONT>                    }<a name="line.869"></a>
<FONT color="green">870</FONT>                    ratio = (f - fopt) / vquad;<a name="line.870"></a>
<FONT color="green">871</FONT>                    final double hDelta = HALF * delta;<a name="line.871"></a>
<FONT color="green">872</FONT>                    if (ratio &lt;= ONE_OVER_TEN) {<a name="line.872"></a>
<FONT color="green">873</FONT>                        // Computing MIN<a name="line.873"></a>
<FONT color="green">874</FONT>                        delta = Math.min(hDelta, dnorm);<a name="line.874"></a>
<FONT color="green">875</FONT>                    } else if (ratio &lt;= .7) {<a name="line.875"></a>
<FONT color="green">876</FONT>                        // Computing MAX<a name="line.876"></a>
<FONT color="green">877</FONT>                        delta = Math.max(hDelta, dnorm);<a name="line.877"></a>
<FONT color="green">878</FONT>                    } else {<a name="line.878"></a>
<FONT color="green">879</FONT>                        // Computing MAX<a name="line.879"></a>
<FONT color="green">880</FONT>                        delta = Math.max(hDelta, 2 * dnorm);<a name="line.880"></a>
<FONT color="green">881</FONT>                    }<a name="line.881"></a>
<FONT color="green">882</FONT>                    if (delta &lt;= rho * 1.5) {<a name="line.882"></a>
<FONT color="green">883</FONT>                        delta = rho;<a name="line.883"></a>
<FONT color="green">884</FONT>                    }<a name="line.884"></a>
<FONT color="green">885</FONT>    <a name="line.885"></a>
<FONT color="green">886</FONT>                    // Recalculate KNEW and DENOM if the new F is less than FOPT.<a name="line.886"></a>
<FONT color="green">887</FONT>    <a name="line.887"></a>
<FONT color="green">888</FONT>                    if (f &lt; fopt) {<a name="line.888"></a>
<FONT color="green">889</FONT>                        final int ksav = knew;<a name="line.889"></a>
<FONT color="green">890</FONT>                        final double densav = denom;<a name="line.890"></a>
<FONT color="green">891</FONT>                        final double delsq = delta * delta;<a name="line.891"></a>
<FONT color="green">892</FONT>                        scaden = ZERO;<a name="line.892"></a>
<FONT color="green">893</FONT>                        biglsq = ZERO;<a name="line.893"></a>
<FONT color="green">894</FONT>                        knew = 0;<a name="line.894"></a>
<FONT color="green">895</FONT>                        for (int k = 0; k &lt; npt; k++) {<a name="line.895"></a>
<FONT color="green">896</FONT>                            double hdiag = ZERO;<a name="line.896"></a>
<FONT color="green">897</FONT>                            for (int m = 0; m &lt; nptm; m++) {<a name="line.897"></a>
<FONT color="green">898</FONT>                                // Computing 2nd power<a name="line.898"></a>
<FONT color="green">899</FONT>                                final double d1 = zMatrix.getEntry(k, m);<a name="line.899"></a>
<FONT color="green">900</FONT>                                hdiag += d1 * d1;<a name="line.900"></a>
<FONT color="green">901</FONT>                            }<a name="line.901"></a>
<FONT color="green">902</FONT>                            // Computing 2nd power<a name="line.902"></a>
<FONT color="green">903</FONT>                            final double d1 = lagrangeValuesAtNewPoint.getEntry(k);<a name="line.903"></a>
<FONT color="green">904</FONT>                            final double den = beta * hdiag + d1 * d1;<a name="line.904"></a>
<FONT color="green">905</FONT>                            distsq = ZERO;<a name="line.905"></a>
<FONT color="green">906</FONT>                            for (int j = 0; j &lt; n; j++) {<a name="line.906"></a>
<FONT color="green">907</FONT>                                // Computing 2nd power<a name="line.907"></a>
<FONT color="green">908</FONT>                                final double d2 = interpolationPoints.getEntry(k, j) - newPoint.getEntry(j);<a name="line.908"></a>
<FONT color="green">909</FONT>                                distsq += d2 * d2;<a name="line.909"></a>
<FONT color="green">910</FONT>                            }<a name="line.910"></a>
<FONT color="green">911</FONT>                            // Computing MAX<a name="line.911"></a>
<FONT color="green">912</FONT>                            // Computing 2nd power<a name="line.912"></a>
<FONT color="green">913</FONT>                            final double d3 = distsq / delsq;<a name="line.913"></a>
<FONT color="green">914</FONT>                            final double temp = Math.max(ONE, d3 * d3);<a name="line.914"></a>
<FONT color="green">915</FONT>                            if (temp * den &gt; scaden) {<a name="line.915"></a>
<FONT color="green">916</FONT>                                scaden = temp * den;<a name="line.916"></a>
<FONT color="green">917</FONT>                                knew = k;<a name="line.917"></a>
<FONT color="green">918</FONT>                                denom = den;<a name="line.918"></a>
<FONT color="green">919</FONT>                            }<a name="line.919"></a>
<FONT color="green">920</FONT>                            // Computing MAX<a name="line.920"></a>
<FONT color="green">921</FONT>                            // Computing 2nd power<a name="line.921"></a>
<FONT color="green">922</FONT>                            final double d4 = lagrangeValuesAtNewPoint.getEntry(k);<a name="line.922"></a>
<FONT color="green">923</FONT>                            final double d5 = temp * (d4 * d4);<a name="line.923"></a>
<FONT color="green">924</FONT>                            biglsq = Math.max(biglsq, d5);<a name="line.924"></a>
<FONT color="green">925</FONT>                        }<a name="line.925"></a>
<FONT color="green">926</FONT>                        if (scaden &lt;= HALF * biglsq) {<a name="line.926"></a>
<FONT color="green">927</FONT>                            knew = ksav;<a name="line.927"></a>
<FONT color="green">928</FONT>                            denom = densav;<a name="line.928"></a>
<FONT color="green">929</FONT>                        }<a name="line.929"></a>
<FONT color="green">930</FONT>                    }<a name="line.930"></a>
<FONT color="green">931</FONT>                }<a name="line.931"></a>
<FONT color="green">932</FONT>    <a name="line.932"></a>
<FONT color="green">933</FONT>                // Update BMAT and ZMAT, so that the KNEW-th interpolation point can be<a name="line.933"></a>
<FONT color="green">934</FONT>                // moved. Also update the second derivative terms of the model.<a name="line.934"></a>
<FONT color="green">935</FONT>    <a name="line.935"></a>
<FONT color="green">936</FONT>                update(beta, denom, knew);<a name="line.936"></a>
<FONT color="green">937</FONT>    <a name="line.937"></a>
<FONT color="green">938</FONT>                ih = 0;<a name="line.938"></a>
<FONT color="green">939</FONT>                final double pqold = modelSecondDerivativesParameters.getEntry(knew);<a name="line.939"></a>
<FONT color="green">940</FONT>                modelSecondDerivativesParameters.setEntry(knew, ZERO);<a name="line.940"></a>
<FONT color="green">941</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.941"></a>
<FONT color="green">942</FONT>                    final double temp = pqold * interpolationPoints.getEntry(knew, i);<a name="line.942"></a>
<FONT color="green">943</FONT>                    for (int j = 0; j &lt;= i; j++) {<a name="line.943"></a>
<FONT color="green">944</FONT>                        modelSecondDerivativesValues.setEntry(ih, modelSecondDerivativesValues.getEntry(ih) + temp * interpolationPoints.getEntry(knew, j));<a name="line.944"></a>
<FONT color="green">945</FONT>                        ih++;<a name="line.945"></a>
<FONT color="green">946</FONT>                    }<a name="line.946"></a>
<FONT color="green">947</FONT>                }<a name="line.947"></a>
<FONT color="green">948</FONT>                for (int m = 0; m &lt; nptm; m++) {<a name="line.948"></a>
<FONT color="green">949</FONT>                    final double temp = diff * zMatrix.getEntry(knew, m);<a name="line.949"></a>
<FONT color="green">950</FONT>                    for (int k = 0; k &lt; npt; k++) {<a name="line.950"></a>
<FONT color="green">951</FONT>                        modelSecondDerivativesParameters.setEntry(k, modelSecondDerivativesParameters.getEntry(k) + temp * zMatrix.getEntry(k, m));<a name="line.951"></a>
<FONT color="green">952</FONT>                    }<a name="line.952"></a>
<FONT color="green">953</FONT>                }<a name="line.953"></a>
<FONT color="green">954</FONT>    <a name="line.954"></a>
<FONT color="green">955</FONT>                // Include the new interpolation point, and make the changes to GOPT at<a name="line.955"></a>
<FONT color="green">956</FONT>                // the old XOPT that are caused by the updating of the quadratic model.<a name="line.956"></a>
<FONT color="green">957</FONT>    <a name="line.957"></a>
<FONT color="green">958</FONT>                fAtInterpolationPoints.setEntry(knew,  f);<a name="line.958"></a>
<FONT color="green">959</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.959"></a>
<FONT color="green">960</FONT>                    interpolationPoints.setEntry(knew, i, newPoint.getEntry(i));<a name="line.960"></a>
<FONT color="green">961</FONT>                    work1.setEntry(i, bMatrix.getEntry(knew, i));<a name="line.961"></a>
<FONT color="green">962</FONT>                }<a name="line.962"></a>
<FONT color="green">963</FONT>                for (int k = 0; k &lt; npt; k++) {<a name="line.963"></a>
<FONT color="green">964</FONT>                    double suma = ZERO;<a name="line.964"></a>
<FONT color="green">965</FONT>                    for (int m = 0; m &lt; nptm; m++) {<a name="line.965"></a>
<FONT color="green">966</FONT>                        suma += zMatrix.getEntry(knew, m) * zMatrix.getEntry(k, m);<a name="line.966"></a>
<FONT color="green">967</FONT>                    }<a name="line.967"></a>
<FONT color="green">968</FONT>                    double sumb = ZERO;<a name="line.968"></a>
<FONT color="green">969</FONT>                    for (int j = 0; j &lt; n; j++) {<a name="line.969"></a>
<FONT color="green">970</FONT>                        sumb += interpolationPoints.getEntry(k, j) * trustRegionCenterOffset.getEntry(j);<a name="line.970"></a>
<FONT color="green">971</FONT>                    }<a name="line.971"></a>
<FONT color="green">972</FONT>                    final double temp = suma * sumb;<a name="line.972"></a>
<FONT color="green">973</FONT>                    for (int i = 0; i &lt; n; i++) {<a name="line.973"></a>
<FONT color="green">974</FONT>                        work1.setEntry(i, work1.getEntry(i) + temp * interpolationPoints.getEntry(k, i));<a name="line.974"></a>
<FONT color="green">975</FONT>                    }<a name="line.975"></a>
<FONT color="green">976</FONT>                }<a name="line.976"></a>
<FONT color="green">977</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.977"></a>
<FONT color="green">978</FONT>                    gradientAtTrustRegionCenter.setEntry(i, gradientAtTrustRegionCenter.getEntry(i) + diff * work1.getEntry(i));<a name="line.978"></a>
<FONT color="green">979</FONT>                }<a name="line.979"></a>
<FONT color="green">980</FONT>    <a name="line.980"></a>
<FONT color="green">981</FONT>                // Update XOPT, GOPT and KOPT if the new calculated F is less than FOPT.<a name="line.981"></a>
<FONT color="green">982</FONT>    <a name="line.982"></a>
<FONT color="green">983</FONT>                if (f &lt; fopt) {<a name="line.983"></a>
<FONT color="green">984</FONT>                    trustRegionCenterInterpolationPointIndex = knew;<a name="line.984"></a>
<FONT color="green">985</FONT>                    xoptsq = ZERO;<a name="line.985"></a>
<FONT color="green">986</FONT>                    ih = 0;<a name="line.986"></a>
<FONT color="green">987</FONT>                    for (int j = 0; j &lt; n; j++) {<a name="line.987"></a>
<FONT color="green">988</FONT>                        trustRegionCenterOffset.setEntry(j, newPoint.getEntry(j));<a name="line.988"></a>
<FONT color="green">989</FONT>                        // Computing 2nd power<a name="line.989"></a>
<FONT color="green">990</FONT>                        final double d1 = trustRegionCenterOffset.getEntry(j);<a name="line.990"></a>
<FONT color="green">991</FONT>                        xoptsq += d1 * d1;<a name="line.991"></a>
<FONT color="green">992</FONT>                        for (int i = 0; i &lt;= j; i++) {<a name="line.992"></a>
<FONT color="green">993</FONT>                            if (i &lt; j) {<a name="line.993"></a>
<FONT color="green">994</FONT>                                gradientAtTrustRegionCenter.setEntry(j, gradientAtTrustRegionCenter.getEntry(j) + modelSecondDerivativesValues.getEntry(ih) * trialStepPoint.getEntry(i));<a name="line.994"></a>
<FONT color="green">995</FONT>                            }<a name="line.995"></a>
<FONT color="green">996</FONT>                            gradientAtTrustRegionCenter.setEntry(i, gradientAtTrustRegionCenter.getEntry(i) + modelSecondDerivativesValues.getEntry(ih) * trialStepPoint.getEntry(j));<a name="line.996"></a>
<FONT color="green">997</FONT>                            ih++;<a name="line.997"></a>
<FONT color="green">998</FONT>                        }<a name="line.998"></a>
<FONT color="green">999</FONT>                    }<a name="line.999"></a>
<FONT color="green">1000</FONT>                    for (int k = 0; k &lt; npt; k++) {<a name="line.1000"></a>
<FONT color="green">1001</FONT>                        double temp = ZERO;<a name="line.1001"></a>
<FONT color="green">1002</FONT>                        for (int j = 0; j &lt; n; j++) {<a name="line.1002"></a>
<FONT color="green">1003</FONT>                            temp += interpolationPoints.getEntry(k, j) * trialStepPoint.getEntry(j);<a name="line.1003"></a>
<FONT color="green">1004</FONT>                        }<a name="line.1004"></a>
<FONT color="green">1005</FONT>                        temp *= modelSecondDerivativesParameters.getEntry(k);<a name="line.1005"></a>
<FONT color="green">1006</FONT>                        for (int i = 0; i &lt; n; i++) {<a name="line.1006"></a>
<FONT color="green">1007</FONT>                            gradientAtTrustRegionCenter.setEntry(i, gradientAtTrustRegionCenter.getEntry(i) + temp * interpolationPoints.getEntry(k, i));<a name="line.1007"></a>
<FONT color="green">1008</FONT>                        }<a name="line.1008"></a>
<FONT color="green">1009</FONT>                    }<a name="line.1009"></a>
<FONT color="green">1010</FONT>                }<a name="line.1010"></a>
<FONT color="green">1011</FONT>    <a name="line.1011"></a>
<FONT color="green">1012</FONT>                // Calculate the parameters of the least Frobenius norm interpolant to<a name="line.1012"></a>
<FONT color="green">1013</FONT>                // the current data, the gradient of this interpolant at XOPT being put<a name="line.1013"></a>
<FONT color="green">1014</FONT>                // into VLAG(NPT+I), I=1,2,...,N.<a name="line.1014"></a>
<FONT color="green">1015</FONT>    <a name="line.1015"></a>
<FONT color="green">1016</FONT>                if (ntrits &gt; 0) {<a name="line.1016"></a>
<FONT color="green">1017</FONT>                    for (int k = 0; k &lt; npt; k++) {<a name="line.1017"></a>
<FONT color="green">1018</FONT>                        lagrangeValuesAtNewPoint.setEntry(k, fAtInterpolationPoints.getEntry(k) - fAtInterpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex));<a name="line.1018"></a>
<FONT color="green">1019</FONT>                        work3.setEntry(k, ZERO);<a name="line.1019"></a>
<FONT color="green">1020</FONT>                    }<a name="line.1020"></a>
<FONT color="green">1021</FONT>                    for (int j = 0; j &lt; nptm; j++) {<a name="line.1021"></a>
<FONT color="green">1022</FONT>                        double sum = ZERO;<a name="line.1022"></a>
<FONT color="green">1023</FONT>                        for (int k = 0; k &lt; npt; k++) {<a name="line.1023"></a>
<FONT color="green">1024</FONT>                            sum += zMatrix.getEntry(k, j) * lagrangeValuesAtNewPoint.getEntry(k);<a name="line.1024"></a>
<FONT color="green">1025</FONT>                        }<a name="line.1025"></a>
<FONT color="green">1026</FONT>                        for (int k = 0; k &lt; npt; k++) {<a name="line.1026"></a>
<FONT color="green">1027</FONT>                            work3.setEntry(k, work3.getEntry(k) + sum * zMatrix.getEntry(k, j));<a name="line.1027"></a>
<FONT color="green">1028</FONT>                        }<a name="line.1028"></a>
<FONT color="green">1029</FONT>                    }<a name="line.1029"></a>
<FONT color="green">1030</FONT>                    for (int k = 0; k &lt; npt; k++) {<a name="line.1030"></a>
<FONT color="green">1031</FONT>                        double sum = ZERO;<a name="line.1031"></a>
<FONT color="green">1032</FONT>                        for (int j = 0; j &lt; n; j++) {<a name="line.1032"></a>
<FONT color="green">1033</FONT>                            sum += interpolationPoints.getEntry(k, j) * trustRegionCenterOffset.getEntry(j);<a name="line.1033"></a>
<FONT color="green">1034</FONT>                        }<a name="line.1034"></a>
<FONT color="green">1035</FONT>                        work2.setEntry(k, work3.getEntry(k));<a name="line.1035"></a>
<FONT color="green">1036</FONT>                        work3.setEntry(k, sum * work3.getEntry(k));<a name="line.1036"></a>
<FONT color="green">1037</FONT>                    }<a name="line.1037"></a>
<FONT color="green">1038</FONT>                    double gqsq = ZERO;<a name="line.1038"></a>
<FONT color="green">1039</FONT>                    double gisq = ZERO;<a name="line.1039"></a>
<FONT color="green">1040</FONT>                    for (int i = 0; i &lt; n; i++) {<a name="line.1040"></a>
<FONT color="green">1041</FONT>                        double sum = ZERO;<a name="line.1041"></a>
<FONT color="green">1042</FONT>                        for (int k = 0; k &lt; npt; k++) {<a name="line.1042"></a>
<FONT color="green">1043</FONT>                            sum += bMatrix.getEntry(k, i) *<a name="line.1043"></a>
<FONT color="green">1044</FONT>                                lagrangeValuesAtNewPoint.getEntry(k) + interpolationPoints.getEntry(k, i) * work3.getEntry(k);<a name="line.1044"></a>
<FONT color="green">1045</FONT>                        }<a name="line.1045"></a>
<FONT color="green">1046</FONT>                        if (trustRegionCenterOffset.getEntry(i) == lowerDifference.getEntry(i)) {<a name="line.1046"></a>
<FONT color="green">1047</FONT>                            // Computing MIN<a name="line.1047"></a>
<FONT color="green">1048</FONT>                            // Computing 2nd power<a name="line.1048"></a>
<FONT color="green">1049</FONT>                            final double d1 = Math.min(ZERO, gradientAtTrustRegionCenter.getEntry(i));<a name="line.1049"></a>
<FONT color="green">1050</FONT>                            gqsq += d1 * d1;<a name="line.1050"></a>
<FONT color="green">1051</FONT>                            // Computing 2nd power<a name="line.1051"></a>
<FONT color="green">1052</FONT>                            final double d2 = Math.min(ZERO, sum);<a name="line.1052"></a>
<FONT color="green">1053</FONT>                            gisq += d2 * d2;<a name="line.1053"></a>
<FONT color="green">1054</FONT>                        } else if (trustRegionCenterOffset.getEntry(i) == upperDifference.getEntry(i)) {<a name="line.1054"></a>
<FONT color="green">1055</FONT>                            // Computing MAX<a name="line.1055"></a>
<FONT color="green">1056</FONT>                            // Computing 2nd power<a name="line.1056"></a>
<FONT color="green">1057</FONT>                            final double d1 = Math.max(ZERO, gradientAtTrustRegionCenter.getEntry(i));<a name="line.1057"></a>
<FONT color="green">1058</FONT>                            gqsq += d1 * d1;<a name="line.1058"></a>
<FONT color="green">1059</FONT>                            // Computing 2nd power<a name="line.1059"></a>
<FONT color="green">1060</FONT>                            final double d2 = Math.max(ZERO, sum);<a name="line.1060"></a>
<FONT color="green">1061</FONT>                            gisq += d2 * d2;<a name="line.1061"></a>
<FONT color="green">1062</FONT>                        } else {<a name="line.1062"></a>
<FONT color="green">1063</FONT>                            // Computing 2nd power<a name="line.1063"></a>
<FONT color="green">1064</FONT>                            final double d1 = gradientAtTrustRegionCenter.getEntry(i);<a name="line.1064"></a>
<FONT color="green">1065</FONT>                            gqsq += d1 * d1;<a name="line.1065"></a>
<FONT color="green">1066</FONT>                            gisq += sum * sum;<a name="line.1066"></a>
<FONT color="green">1067</FONT>                        }<a name="line.1067"></a>
<FONT color="green">1068</FONT>                        lagrangeValuesAtNewPoint.setEntry(npt + i, sum);<a name="line.1068"></a>
<FONT color="green">1069</FONT>                    }<a name="line.1069"></a>
<FONT color="green">1070</FONT>    <a name="line.1070"></a>
<FONT color="green">1071</FONT>                    // Test whether to replace the new quadratic model by the least Frobenius<a name="line.1071"></a>
<FONT color="green">1072</FONT>                    // norm interpolant, making the replacement if the test is satisfied.<a name="line.1072"></a>
<FONT color="green">1073</FONT>    <a name="line.1073"></a>
<FONT color="green">1074</FONT>                    ++itest;<a name="line.1074"></a>
<FONT color="green">1075</FONT>                    if (gqsq &lt; TEN * gisq) {<a name="line.1075"></a>
<FONT color="green">1076</FONT>                        itest = 0;<a name="line.1076"></a>
<FONT color="green">1077</FONT>                    }<a name="line.1077"></a>
<FONT color="green">1078</FONT>                    if (itest &gt;= 3) {<a name="line.1078"></a>
<FONT color="green">1079</FONT>                        for (int i = 0, max = Math.max(npt, nh); i &lt; max; i++) {<a name="line.1079"></a>
<FONT color="green">1080</FONT>                            if (i &lt; n) {<a name="line.1080"></a>
<FONT color="green">1081</FONT>                                gradientAtTrustRegionCenter.setEntry(i, lagrangeValuesAtNewPoint.getEntry(npt + i));<a name="line.1081"></a>
<FONT color="green">1082</FONT>                            }<a name="line.1082"></a>
<FONT color="green">1083</FONT>                            if (i &lt; npt) {<a name="line.1083"></a>
<FONT color="green">1084</FONT>                                modelSecondDerivativesParameters.setEntry(i, work2.getEntry(i));<a name="line.1084"></a>
<FONT color="green">1085</FONT>                            }<a name="line.1085"></a>
<FONT color="green">1086</FONT>                            if (i &lt; nh) {<a name="line.1086"></a>
<FONT color="green">1087</FONT>                                modelSecondDerivativesValues.setEntry(i, ZERO);<a name="line.1087"></a>
<FONT color="green">1088</FONT>                            }<a name="line.1088"></a>
<FONT color="green">1089</FONT>                            itest = 0;<a name="line.1089"></a>
<FONT color="green">1090</FONT>                        }<a name="line.1090"></a>
<FONT color="green">1091</FONT>                    }<a name="line.1091"></a>
<FONT color="green">1092</FONT>                }<a name="line.1092"></a>
<FONT color="green">1093</FONT>    <a name="line.1093"></a>
<FONT color="green">1094</FONT>                // If a trust region step has provided a sufficient decrease in F, then<a name="line.1094"></a>
<FONT color="green">1095</FONT>                // branch for another trust region calculation. The case NTRITS=0 occurs<a name="line.1095"></a>
<FONT color="green">1096</FONT>                // when the new interpolation point was reached by an alternative step.<a name="line.1096"></a>
<FONT color="green">1097</FONT>    <a name="line.1097"></a>
<FONT color="green">1098</FONT>                if (ntrits == 0) {<a name="line.1098"></a>
<FONT color="green">1099</FONT>                    state = 60; break;<a name="line.1099"></a>
<FONT color="green">1100</FONT>                }<a name="line.1100"></a>
<FONT color="green">1101</FONT>                if (f &lt;= fopt + ONE_OVER_TEN * vquad) {<a name="line.1101"></a>
<FONT color="green">1102</FONT>                    state = 60; break;<a name="line.1102"></a>
<FONT color="green">1103</FONT>                }<a name="line.1103"></a>
<FONT color="green">1104</FONT>    <a name="line.1104"></a>
<FONT color="green">1105</FONT>                // Alternatively, find out if the interpolation points are close enough<a name="line.1105"></a>
<FONT color="green">1106</FONT>                //   to the best point so far.<a name="line.1106"></a>
<FONT color="green">1107</FONT>    <a name="line.1107"></a>
<FONT color="green">1108</FONT>                // Computing MAX<a name="line.1108"></a>
<FONT color="green">1109</FONT>                // Computing 2nd power<a name="line.1109"></a>
<FONT color="green">1110</FONT>                final double d1 = TWO * delta;<a name="line.1110"></a>
<FONT color="green">1111</FONT>                // Computing 2nd power<a name="line.1111"></a>
<FONT color="green">1112</FONT>                final double d2 = TEN * rho;<a name="line.1112"></a>
<FONT color="green">1113</FONT>                distsq = Math.max(d1 * d1, d2 * d2);<a name="line.1113"></a>
<FONT color="green">1114</FONT>            }<a name="line.1114"></a>
<FONT color="green">1115</FONT>            case 650: {<a name="line.1115"></a>
<FONT color="green">1116</FONT>                printState(650); // XXX<a name="line.1116"></a>
<FONT color="green">1117</FONT>                knew = -1;<a name="line.1117"></a>
<FONT color="green">1118</FONT>                for (int k = 0; k &lt; npt; k++) {<a name="line.1118"></a>
<FONT color="green">1119</FONT>                    double sum = ZERO;<a name="line.1119"></a>
<FONT color="green">1120</FONT>                    for (int j = 0; j &lt; n; j++) {<a name="line.1120"></a>
<FONT color="green">1121</FONT>                        // Computing 2nd power<a name="line.1121"></a>
<FONT color="green">1122</FONT>                        final double d1 = interpolationPoints.getEntry(k, j) - trustRegionCenterOffset.getEntry(j);<a name="line.1122"></a>
<FONT color="green">1123</FONT>                        sum += d1 * d1;<a name="line.1123"></a>
<FONT color="green">1124</FONT>                    }<a name="line.1124"></a>
<FONT color="green">1125</FONT>                    if (sum &gt; distsq) {<a name="line.1125"></a>
<FONT color="green">1126</FONT>                        knew = k;<a name="line.1126"></a>
<FONT color="green">1127</FONT>                        distsq = sum;<a name="line.1127"></a>
<FONT color="green">1128</FONT>                    }<a name="line.1128"></a>
<FONT color="green">1129</FONT>                }<a name="line.1129"></a>
<FONT color="green">1130</FONT>    <a name="line.1130"></a>
<FONT color="green">1131</FONT>                // If KNEW is positive, then ALTMOV finds alternative new positions for<a name="line.1131"></a>
<FONT color="green">1132</FONT>                // the KNEW-th interpolation point within distance ADELT of XOPT. It is<a name="line.1132"></a>
<FONT color="green">1133</FONT>                // reached via label 90. Otherwise, there is a branch to label 60 for<a name="line.1133"></a>
<FONT color="green">1134</FONT>                // another trust region iteration, unless the calculations with the<a name="line.1134"></a>
<FONT color="green">1135</FONT>                // current RHO are complete.<a name="line.1135"></a>
<FONT color="green">1136</FONT>    <a name="line.1136"></a>
<FONT color="green">1137</FONT>                if (knew &gt;= 0) {<a name="line.1137"></a>
<FONT color="green">1138</FONT>                    final double dist = Math.sqrt(distsq);<a name="line.1138"></a>
<FONT color="green">1139</FONT>                    if (ntrits == -1) {<a name="line.1139"></a>
<FONT color="green">1140</FONT>                        // Computing MIN<a name="line.1140"></a>
<FONT color="green">1141</FONT>                        delta = Math.min(ONE_OVER_TEN * delta, HALF * dist);<a name="line.1141"></a>
<FONT color="green">1142</FONT>                        if (delta &lt;= rho * 1.5) {<a name="line.1142"></a>
<FONT color="green">1143</FONT>                            delta = rho;<a name="line.1143"></a>
<FONT color="green">1144</FONT>                        }<a name="line.1144"></a>
<FONT color="green">1145</FONT>                    }<a name="line.1145"></a>
<FONT color="green">1146</FONT>                    ntrits = 0;<a name="line.1146"></a>
<FONT color="green">1147</FONT>                    // Computing MAX<a name="line.1147"></a>
<FONT color="green">1148</FONT>                    // Computing MIN<a name="line.1148"></a>
<FONT color="green">1149</FONT>                    final double d1 = Math.min(ONE_OVER_TEN * dist, delta);<a name="line.1149"></a>
<FONT color="green">1150</FONT>                    adelt = Math.max(d1, rho);<a name="line.1150"></a>
<FONT color="green">1151</FONT>                    dsq = adelt * adelt;<a name="line.1151"></a>
<FONT color="green">1152</FONT>                    state = 90; break;<a name="line.1152"></a>
<FONT color="green">1153</FONT>                }<a name="line.1153"></a>
<FONT color="green">1154</FONT>                if (ntrits == -1) {<a name="line.1154"></a>
<FONT color="green">1155</FONT>                    state = 680; break;<a name="line.1155"></a>
<FONT color="green">1156</FONT>                }<a name="line.1156"></a>
<FONT color="green">1157</FONT>                if (ratio &gt; ZERO) {<a name="line.1157"></a>
<FONT color="green">1158</FONT>                    state = 60; break;<a name="line.1158"></a>
<FONT color="green">1159</FONT>                }<a name="line.1159"></a>
<FONT color="green">1160</FONT>                if (Math.max(delta, dnorm) &gt; rho) {<a name="line.1160"></a>
<FONT color="green">1161</FONT>                    state = 60; break;<a name="line.1161"></a>
<FONT color="green">1162</FONT>                }<a name="line.1162"></a>
<FONT color="green">1163</FONT>    <a name="line.1163"></a>
<FONT color="green">1164</FONT>                // The calculations with the current value of RHO are complete. Pick the<a name="line.1164"></a>
<FONT color="green">1165</FONT>                //   next values of RHO and DELTA.<a name="line.1165"></a>
<FONT color="green">1166</FONT>            }<a name="line.1166"></a>
<FONT color="green">1167</FONT>            case 680: {<a name="line.1167"></a>
<FONT color="green">1168</FONT>                printState(680); // XXX<a name="line.1168"></a>
<FONT color="green">1169</FONT>                if (rho &gt; stoppingTrustRegionRadius) {<a name="line.1169"></a>
<FONT color="green">1170</FONT>                    delta = HALF * rho;<a name="line.1170"></a>
<FONT color="green">1171</FONT>                    ratio = rho / stoppingTrustRegionRadius;<a name="line.1171"></a>
<FONT color="green">1172</FONT>                    if (ratio &lt;= SIXTEEN) {<a name="line.1172"></a>
<FONT color="green">1173</FONT>                        rho = stoppingTrustRegionRadius;<a name="line.1173"></a>
<FONT color="green">1174</FONT>                    } else if (ratio &lt;= TWO_HUNDRED_FIFTY) {<a name="line.1174"></a>
<FONT color="green">1175</FONT>                        rho = Math.sqrt(ratio) * stoppingTrustRegionRadius;<a name="line.1175"></a>
<FONT color="green">1176</FONT>                    } else {<a name="line.1176"></a>
<FONT color="green">1177</FONT>                        rho *= ONE_OVER_TEN;<a name="line.1177"></a>
<FONT color="green">1178</FONT>                    }<a name="line.1178"></a>
<FONT color="green">1179</FONT>                    delta = Math.max(delta, rho);<a name="line.1179"></a>
<FONT color="green">1180</FONT>                    ntrits = 0;<a name="line.1180"></a>
<FONT color="green">1181</FONT>                    nfsav = getEvaluations();<a name="line.1181"></a>
<FONT color="green">1182</FONT>                    state = 60; break;<a name="line.1182"></a>
<FONT color="green">1183</FONT>                }<a name="line.1183"></a>
<FONT color="green">1184</FONT>    <a name="line.1184"></a>
<FONT color="green">1185</FONT>                // Return from the calculation, after another Newton-Raphson step, if<a name="line.1185"></a>
<FONT color="green">1186</FONT>                //   it is too short to have been tried before.<a name="line.1186"></a>
<FONT color="green">1187</FONT>    <a name="line.1187"></a>
<FONT color="green">1188</FONT>                if (ntrits == -1) {<a name="line.1188"></a>
<FONT color="green">1189</FONT>                    state = 360; break;<a name="line.1189"></a>
<FONT color="green">1190</FONT>                }<a name="line.1190"></a>
<FONT color="green">1191</FONT>            }<a name="line.1191"></a>
<FONT color="green">1192</FONT>            case 720: {<a name="line.1192"></a>
<FONT color="green">1193</FONT>                printState(720); // XXX<a name="line.1193"></a>
<FONT color="green">1194</FONT>                if (fAtInterpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex) &lt;= fsave) {<a name="line.1194"></a>
<FONT color="green">1195</FONT>                    for (int i = 0; i &lt; n; i++) {<a name="line.1195"></a>
<FONT color="green">1196</FONT>                        // Computing MIN<a name="line.1196"></a>
<FONT color="green">1197</FONT>                        // Computing MAX<a name="line.1197"></a>
<FONT color="green">1198</FONT>                        final double d3 = lowerBound[i];<a name="line.1198"></a>
<FONT color="green">1199</FONT>                        final double d4 = originShift.getEntry(i) + trustRegionCenterOffset.getEntry(i);<a name="line.1199"></a>
<FONT color="green">1200</FONT>                        final double d1 = Math.max(d3, d4);<a name="line.1200"></a>
<FONT color="green">1201</FONT>                        final double d2 = upperBound[i];<a name="line.1201"></a>
<FONT color="green">1202</FONT>                        currentBest.setEntry(i, Math.min(d1, d2));<a name="line.1202"></a>
<FONT color="green">1203</FONT>                        if (trustRegionCenterOffset.getEntry(i) == lowerDifference.getEntry(i)) {<a name="line.1203"></a>
<FONT color="green">1204</FONT>                            currentBest.setEntry(i, lowerBound[i]);<a name="line.1204"></a>
<FONT color="green">1205</FONT>                        }<a name="line.1205"></a>
<FONT color="green">1206</FONT>                        if (trustRegionCenterOffset.getEntry(i) == upperDifference.getEntry(i)) {<a name="line.1206"></a>
<FONT color="green">1207</FONT>                            currentBest.setEntry(i, upperBound[i]);<a name="line.1207"></a>
<FONT color="green">1208</FONT>                        }<a name="line.1208"></a>
<FONT color="green">1209</FONT>                    }<a name="line.1209"></a>
<FONT color="green">1210</FONT>                    f = fAtInterpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex);<a name="line.1210"></a>
<FONT color="green">1211</FONT>                }<a name="line.1211"></a>
<FONT color="green">1212</FONT>                return f;<a name="line.1212"></a>
<FONT color="green">1213</FONT>            }<a name="line.1213"></a>
<FONT color="green">1214</FONT>            default: {<a name="line.1214"></a>
<FONT color="green">1215</FONT>                throw new MathIllegalStateException(LocalizedFormats.SIMPLE_MESSAGE, "bobyqb");<a name="line.1215"></a>
<FONT color="green">1216</FONT>            }}<a name="line.1216"></a>
<FONT color="green">1217</FONT>        } // bobyqb<a name="line.1217"></a>
<FONT color="green">1218</FONT>    <a name="line.1218"></a>
<FONT color="green">1219</FONT>        // ----------------------------------------------------------------------------------------<a name="line.1219"></a>
<FONT color="green">1220</FONT>    <a name="line.1220"></a>
<FONT color="green">1221</FONT>        /**<a name="line.1221"></a>
<FONT color="green">1222</FONT>         *     The arguments N, NPT, XPT, XOPT, BMAT, ZMAT, NDIM, SL and SU all have<a name="line.1222"></a>
<FONT color="green">1223</FONT>         *       the same meanings as the corresponding arguments of BOBYQB.<a name="line.1223"></a>
<FONT color="green">1224</FONT>         *     KOPT is the index of the optimal interpolation point.<a name="line.1224"></a>
<FONT color="green">1225</FONT>         *     KNEW is the index of the interpolation point that is going to be moved.<a name="line.1225"></a>
<FONT color="green">1226</FONT>         *     ADELT is the current trust region bound.<a name="line.1226"></a>
<FONT color="green">1227</FONT>         *     XNEW will be set to a suitable new position for the interpolation point<a name="line.1227"></a>
<FONT color="green">1228</FONT>         *       XPT(KNEW,.). Specifically, it satisfies the SL, SU and trust region<a name="line.1228"></a>
<FONT color="green">1229</FONT>         *       bounds and it should provide a large denominator in the next call of<a name="line.1229"></a>
<FONT color="green">1230</FONT>         *       UPDATE. The step XNEW-XOPT from XOPT is restricted to moves along the<a name="line.1230"></a>
<FONT color="green">1231</FONT>         *       straight lines through XOPT and another interpolation point.<a name="line.1231"></a>
<FONT color="green">1232</FONT>         *     XALT also provides a large value of the modulus of the KNEW-th Lagrange<a name="line.1232"></a>
<FONT color="green">1233</FONT>         *       function subject to the constraints that have been mentioned, its main<a name="line.1233"></a>
<FONT color="green">1234</FONT>         *       difference from XNEW being that XALT-XOPT is a constrained version of<a name="line.1234"></a>
<FONT color="green">1235</FONT>         *       the Cauchy step within the trust region. An exception is that XALT is<a name="line.1235"></a>
<FONT color="green">1236</FONT>         *       not calculated if all components of GLAG (see below) are zero.<a name="line.1236"></a>
<FONT color="green">1237</FONT>         *     ALPHA will be set to the KNEW-th diagonal element of the H matrix.<a name="line.1237"></a>
<FONT color="green">1238</FONT>         *     CAUCHY will be set to the square of the KNEW-th Lagrange function at<a name="line.1238"></a>
<FONT color="green">1239</FONT>         *       the step XALT-XOPT from XOPT for the vector XALT that is returned,<a name="line.1239"></a>
<FONT color="green">1240</FONT>         *       except that CAUCHY is set to zero if XALT is not calculated.<a name="line.1240"></a>
<FONT color="green">1241</FONT>         *     GLAG is a working space vector of length N for the gradient of the<a name="line.1241"></a>
<FONT color="green">1242</FONT>         *       KNEW-th Lagrange function at XOPT.<a name="line.1242"></a>
<FONT color="green">1243</FONT>         *     HCOL is a working space vector of length NPT for the second derivative<a name="line.1243"></a>
<FONT color="green">1244</FONT>         *       coefficients of the KNEW-th Lagrange function.<a name="line.1244"></a>
<FONT color="green">1245</FONT>         *     W is a working space vector of length 2N that is going to hold the<a name="line.1245"></a>
<FONT color="green">1246</FONT>         *       constrained Cauchy step from XOPT of the Lagrange function, followed<a name="line.1246"></a>
<FONT color="green">1247</FONT>         *       by the downhill version of XALT when the uphill step is calculated.<a name="line.1247"></a>
<FONT color="green">1248</FONT>         *<a name="line.1248"></a>
<FONT color="green">1249</FONT>         *     Set the first NPT components of W to the leading elements of the<a name="line.1249"></a>
<FONT color="green">1250</FONT>         *     KNEW-th column of the H matrix.<a name="line.1250"></a>
<FONT color="green">1251</FONT>         * @param knew<a name="line.1251"></a>
<FONT color="green">1252</FONT>         * @param adelt<a name="line.1252"></a>
<FONT color="green">1253</FONT>         */<a name="line.1253"></a>
<FONT color="green">1254</FONT>        private double[] altmov(<a name="line.1254"></a>
<FONT color="green">1255</FONT>                int knew,<a name="line.1255"></a>
<FONT color="green">1256</FONT>                double adelt<a name="line.1256"></a>
<FONT color="green">1257</FONT>        ) {<a name="line.1257"></a>
<FONT color="green">1258</FONT>            printMethod(); // XXX<a name="line.1258"></a>
<FONT color="green">1259</FONT>    <a name="line.1259"></a>
<FONT color="green">1260</FONT>            final int n = currentBest.getDimension();<a name="line.1260"></a>
<FONT color="green">1261</FONT>            final int npt = numberOfInterpolationPoints;<a name="line.1261"></a>
<FONT color="green">1262</FONT>    <a name="line.1262"></a>
<FONT color="green">1263</FONT>            final ArrayRealVector glag = new ArrayRealVector(n);<a name="line.1263"></a>
<FONT color="green">1264</FONT>            final ArrayRealVector hcol = new ArrayRealVector(npt);<a name="line.1264"></a>
<FONT color="green">1265</FONT>    <a name="line.1265"></a>
<FONT color="green">1266</FONT>            final ArrayRealVector work1 = new ArrayRealVector(n);<a name="line.1266"></a>
<FONT color="green">1267</FONT>            final ArrayRealVector work2 = new ArrayRealVector(n);<a name="line.1267"></a>
<FONT color="green">1268</FONT>    <a name="line.1268"></a>
<FONT color="green">1269</FONT>            for (int k = 0; k &lt; npt; k++) {<a name="line.1269"></a>
<FONT color="green">1270</FONT>                hcol.setEntry(k, ZERO);<a name="line.1270"></a>
<FONT color="green">1271</FONT>            }<a name="line.1271"></a>
<FONT color="green">1272</FONT>            for (int j = 0, max = npt - n - 1; j &lt; max; j++) {<a name="line.1272"></a>
<FONT color="green">1273</FONT>                final double tmp = zMatrix.getEntry(knew, j);<a name="line.1273"></a>
<FONT color="green">1274</FONT>                for (int k = 0; k &lt; npt; k++) {<a name="line.1274"></a>
<FONT color="green">1275</FONT>                    hcol.setEntry(k, hcol.getEntry(k) + tmp * zMatrix.getEntry(k, j));<a name="line.1275"></a>
<FONT color="green">1276</FONT>                }<a name="line.1276"></a>
<FONT color="green">1277</FONT>            }<a name="line.1277"></a>
<FONT color="green">1278</FONT>            final double alpha = hcol.getEntry(knew);<a name="line.1278"></a>
<FONT color="green">1279</FONT>            final double ha = HALF * alpha;<a name="line.1279"></a>
<FONT color="green">1280</FONT>    <a name="line.1280"></a>
<FONT color="green">1281</FONT>            // Calculate the gradient of the KNEW-th Lagrange function at XOPT.<a name="line.1281"></a>
<FONT color="green">1282</FONT>    <a name="line.1282"></a>
<FONT color="green">1283</FONT>            for (int i = 0; i &lt; n; i++) {<a name="line.1283"></a>
<FONT color="green">1284</FONT>                glag.setEntry(i, bMatrix.getEntry(knew, i));<a name="line.1284"></a>
<FONT color="green">1285</FONT>            }<a name="line.1285"></a>
<FONT color="green">1286</FONT>            for (int k = 0; k &lt; npt; k++) {<a name="line.1286"></a>
<FONT color="green">1287</FONT>                double tmp = ZERO;<a name="line.1287"></a>
<FONT color="green">1288</FONT>                for (int j = 0; j &lt; n; j++) {<a name="line.1288"></a>
<FONT color="green">1289</FONT>                    tmp += interpolationPoints.getEntry(k, j) * trustRegionCenterOffset.getEntry(j);<a name="line.1289"></a>
<FONT color="green">1290</FONT>                }<a name="line.1290"></a>
<FONT color="green">1291</FONT>                tmp *= hcol.getEntry(k);<a name="line.1291"></a>
<FONT color="green">1292</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.1292"></a>
<FONT color="green">1293</FONT>                    glag.setEntry(i, glag.getEntry(i) + tmp * interpolationPoints.getEntry(k, i));<a name="line.1293"></a>
<FONT color="green">1294</FONT>                }<a name="line.1294"></a>
<FONT color="green">1295</FONT>            }<a name="line.1295"></a>
<FONT color="green">1296</FONT>    <a name="line.1296"></a>
<FONT color="green">1297</FONT>            // Search for a large denominator along the straight lines through XOPT<a name="line.1297"></a>
<FONT color="green">1298</FONT>            // and another interpolation point. SLBD and SUBD will be lower and upper<a name="line.1298"></a>
<FONT color="green">1299</FONT>            // bounds on the step along each of these lines in turn. PREDSQ will be<a name="line.1299"></a>
<FONT color="green">1300</FONT>            // set to the square of the predicted denominator for each line. PRESAV<a name="line.1300"></a>
<FONT color="green">1301</FONT>            // will be set to the largest admissible value of PREDSQ that occurs.<a name="line.1301"></a>
<FONT color="green">1302</FONT>    <a name="line.1302"></a>
<FONT color="green">1303</FONT>            double presav = ZERO;<a name="line.1303"></a>
<FONT color="green">1304</FONT>            double step = Double.NaN;<a name="line.1304"></a>
<FONT color="green">1305</FONT>            int ksav = 0;<a name="line.1305"></a>
<FONT color="green">1306</FONT>            int ibdsav = 0;<a name="line.1306"></a>
<FONT color="green">1307</FONT>            double stpsav = 0;<a name="line.1307"></a>
<FONT color="green">1308</FONT>            for (int k = 0; k &lt; npt; k++) {<a name="line.1308"></a>
<FONT color="green">1309</FONT>                if (k == trustRegionCenterInterpolationPointIndex) {<a name="line.1309"></a>
<FONT color="green">1310</FONT>                    continue;<a name="line.1310"></a>
<FONT color="green">1311</FONT>                }<a name="line.1311"></a>
<FONT color="green">1312</FONT>                double dderiv = ZERO;<a name="line.1312"></a>
<FONT color="green">1313</FONT>                double distsq = ZERO;<a name="line.1313"></a>
<FONT color="green">1314</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.1314"></a>
<FONT color="green">1315</FONT>                    final double tmp = interpolationPoints.getEntry(k, i) - trustRegionCenterOffset.getEntry(i);<a name="line.1315"></a>
<FONT color="green">1316</FONT>                    dderiv += glag.getEntry(i) * tmp;<a name="line.1316"></a>
<FONT color="green">1317</FONT>                    distsq += tmp * tmp;<a name="line.1317"></a>
<FONT color="green">1318</FONT>                }<a name="line.1318"></a>
<FONT color="green">1319</FONT>                double subd = adelt / Math.sqrt(distsq);<a name="line.1319"></a>
<FONT color="green">1320</FONT>                double slbd = -subd;<a name="line.1320"></a>
<FONT color="green">1321</FONT>                int ilbd = 0;<a name="line.1321"></a>
<FONT color="green">1322</FONT>                int iubd = 0;<a name="line.1322"></a>
<FONT color="green">1323</FONT>                final double sumin = Math.min(ONE, subd);<a name="line.1323"></a>
<FONT color="green">1324</FONT>    <a name="line.1324"></a>
<FONT color="green">1325</FONT>                // Revise SLBD and SUBD if necessary because of the bounds in SL and SU.<a name="line.1325"></a>
<FONT color="green">1326</FONT>    <a name="line.1326"></a>
<FONT color="green">1327</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.1327"></a>
<FONT color="green">1328</FONT>                    final double tmp = interpolationPoints.getEntry(k, i) - trustRegionCenterOffset.getEntry(i);<a name="line.1328"></a>
<FONT color="green">1329</FONT>                    if (tmp &gt; ZERO) {<a name="line.1329"></a>
<FONT color="green">1330</FONT>                        if (slbd * tmp &lt; lowerDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)) {<a name="line.1330"></a>
<FONT color="green">1331</FONT>                            slbd = (lowerDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)) / tmp;<a name="line.1331"></a>
<FONT color="green">1332</FONT>                            ilbd = -i - 1;<a name="line.1332"></a>
<FONT color="green">1333</FONT>                        }<a name="line.1333"></a>
<FONT color="green">1334</FONT>                        if (subd * tmp &gt; upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)) {<a name="line.1334"></a>
<FONT color="green">1335</FONT>                            // Computing MAX<a name="line.1335"></a>
<FONT color="green">1336</FONT>                            subd = Math.max(sumin,<a name="line.1336"></a>
<FONT color="green">1337</FONT>                                            (upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)) / tmp);<a name="line.1337"></a>
<FONT color="green">1338</FONT>                            iubd = i + 1;<a name="line.1338"></a>
<FONT color="green">1339</FONT>                        }<a name="line.1339"></a>
<FONT color="green">1340</FONT>                    } else if (tmp &lt; ZERO) {<a name="line.1340"></a>
<FONT color="green">1341</FONT>                        if (slbd * tmp &gt; upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)) {<a name="line.1341"></a>
<FONT color="green">1342</FONT>                            slbd = (upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)) / tmp;<a name="line.1342"></a>
<FONT color="green">1343</FONT>                            ilbd = i + 1;<a name="line.1343"></a>
<FONT color="green">1344</FONT>                        }<a name="line.1344"></a>
<FONT color="green">1345</FONT>                        if (subd * tmp &lt; lowerDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)) {<a name="line.1345"></a>
<FONT color="green">1346</FONT>                            // Computing MAX<a name="line.1346"></a>
<FONT color="green">1347</FONT>                            subd = Math.max(sumin,<a name="line.1347"></a>
<FONT color="green">1348</FONT>                                            (lowerDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)) / tmp);<a name="line.1348"></a>
<FONT color="green">1349</FONT>                            iubd = -i - 1;<a name="line.1349"></a>
<FONT color="green">1350</FONT>                        }<a name="line.1350"></a>
<FONT color="green">1351</FONT>                    }<a name="line.1351"></a>
<FONT color="green">1352</FONT>                }<a name="line.1352"></a>
<FONT color="green">1353</FONT>    <a name="line.1353"></a>
<FONT color="green">1354</FONT>                // Seek a large modulus of the KNEW-th Lagrange function when the index<a name="line.1354"></a>
<FONT color="green">1355</FONT>                // of the other interpolation point on the line through XOPT is KNEW.<a name="line.1355"></a>
<FONT color="green">1356</FONT>    <a name="line.1356"></a>
<FONT color="green">1357</FONT>                step = slbd;<a name="line.1357"></a>
<FONT color="green">1358</FONT>                int isbd = ilbd;<a name="line.1358"></a>
<FONT color="green">1359</FONT>                double vlag = Double.NaN;<a name="line.1359"></a>
<FONT color="green">1360</FONT>                if (k == knew) {<a name="line.1360"></a>
<FONT color="green">1361</FONT>                    final double diff = dderiv - ONE;<a name="line.1361"></a>
<FONT color="green">1362</FONT>                    vlag = slbd * (dderiv - slbd * diff);<a name="line.1362"></a>
<FONT color="green">1363</FONT>                    final double d1 = subd * (dderiv - subd * diff);<a name="line.1363"></a>
<FONT color="green">1364</FONT>                    if (Math.abs(d1) &gt; Math.abs(vlag)) {<a name="line.1364"></a>
<FONT color="green">1365</FONT>                        step = subd;<a name="line.1365"></a>
<FONT color="green">1366</FONT>                        vlag = d1;<a name="line.1366"></a>
<FONT color="green">1367</FONT>                        isbd = iubd;<a name="line.1367"></a>
<FONT color="green">1368</FONT>                    }<a name="line.1368"></a>
<FONT color="green">1369</FONT>                    final double d2 = HALF * dderiv;<a name="line.1369"></a>
<FONT color="green">1370</FONT>                    final double d3 = d2 - diff * slbd;<a name="line.1370"></a>
<FONT color="green">1371</FONT>                    final double d4 = d2 - diff * subd;<a name="line.1371"></a>
<FONT color="green">1372</FONT>                    if (d3 * d4 &lt; ZERO) {<a name="line.1372"></a>
<FONT color="green">1373</FONT>                        final double d5 = d2 * d2 / diff;<a name="line.1373"></a>
<FONT color="green">1374</FONT>                        if (Math.abs(d5) &gt; Math.abs(vlag)) {<a name="line.1374"></a>
<FONT color="green">1375</FONT>                            step = d2 / diff;<a name="line.1375"></a>
<FONT color="green">1376</FONT>                            vlag = d5;<a name="line.1376"></a>
<FONT color="green">1377</FONT>                            isbd = 0;<a name="line.1377"></a>
<FONT color="green">1378</FONT>                        }<a name="line.1378"></a>
<FONT color="green">1379</FONT>                    }<a name="line.1379"></a>
<FONT color="green">1380</FONT>    <a name="line.1380"></a>
<FONT color="green">1381</FONT>                    // Search along each of the other lines through XOPT and another point.<a name="line.1381"></a>
<FONT color="green">1382</FONT>    <a name="line.1382"></a>
<FONT color="green">1383</FONT>                } else {<a name="line.1383"></a>
<FONT color="green">1384</FONT>                    vlag = slbd * (ONE - slbd);<a name="line.1384"></a>
<FONT color="green">1385</FONT>                    final double tmp = subd * (ONE - subd);<a name="line.1385"></a>
<FONT color="green">1386</FONT>                    if (Math.abs(tmp) &gt; Math.abs(vlag)) {<a name="line.1386"></a>
<FONT color="green">1387</FONT>                        step = subd;<a name="line.1387"></a>
<FONT color="green">1388</FONT>                        vlag = tmp;<a name="line.1388"></a>
<FONT color="green">1389</FONT>                        isbd = iubd;<a name="line.1389"></a>
<FONT color="green">1390</FONT>                    }<a name="line.1390"></a>
<FONT color="green">1391</FONT>                    if (subd &gt; HALF) {<a name="line.1391"></a>
<FONT color="green">1392</FONT>                        if (Math.abs(vlag) &lt; ONE_OVER_FOUR) {<a name="line.1392"></a>
<FONT color="green">1393</FONT>                            step = HALF;<a name="line.1393"></a>
<FONT color="green">1394</FONT>                            vlag = ONE_OVER_FOUR;<a name="line.1394"></a>
<FONT color="green">1395</FONT>                            isbd = 0;<a name="line.1395"></a>
<FONT color="green">1396</FONT>                        }<a name="line.1396"></a>
<FONT color="green">1397</FONT>                    }<a name="line.1397"></a>
<FONT color="green">1398</FONT>                    vlag *= dderiv;<a name="line.1398"></a>
<FONT color="green">1399</FONT>                }<a name="line.1399"></a>
<FONT color="green">1400</FONT>    <a name="line.1400"></a>
<FONT color="green">1401</FONT>                // Calculate PREDSQ for the current line search and maintain PRESAV.<a name="line.1401"></a>
<FONT color="green">1402</FONT>    <a name="line.1402"></a>
<FONT color="green">1403</FONT>                final double tmp = step * (ONE - step) * distsq;<a name="line.1403"></a>
<FONT color="green">1404</FONT>                final double predsq = vlag * vlag * (vlag * vlag + ha * tmp * tmp);<a name="line.1404"></a>
<FONT color="green">1405</FONT>                if (predsq &gt; presav) {<a name="line.1405"></a>
<FONT color="green">1406</FONT>                    presav = predsq;<a name="line.1406"></a>
<FONT color="green">1407</FONT>                    ksav = k;<a name="line.1407"></a>
<FONT color="green">1408</FONT>                    stpsav = step;<a name="line.1408"></a>
<FONT color="green">1409</FONT>                    ibdsav = isbd;<a name="line.1409"></a>
<FONT color="green">1410</FONT>                }<a name="line.1410"></a>
<FONT color="green">1411</FONT>            }<a name="line.1411"></a>
<FONT color="green">1412</FONT>    <a name="line.1412"></a>
<FONT color="green">1413</FONT>            // Construct XNEW in a way that satisfies the bound constraints exactly.<a name="line.1413"></a>
<FONT color="green">1414</FONT>    <a name="line.1414"></a>
<FONT color="green">1415</FONT>            for (int i = 0; i &lt; n; i++) {<a name="line.1415"></a>
<FONT color="green">1416</FONT>                final double tmp = trustRegionCenterOffset.getEntry(i) + stpsav * (interpolationPoints.getEntry(ksav, i) - trustRegionCenterOffset.getEntry(i));<a name="line.1416"></a>
<FONT color="green">1417</FONT>                newPoint.setEntry(i, Math.max(lowerDifference.getEntry(i),<a name="line.1417"></a>
<FONT color="green">1418</FONT>                                          Math.min(upperDifference.getEntry(i), tmp)));<a name="line.1418"></a>
<FONT color="green">1419</FONT>            }<a name="line.1419"></a>
<FONT color="green">1420</FONT>            if (ibdsav &lt; 0) {<a name="line.1420"></a>
<FONT color="green">1421</FONT>                newPoint.setEntry(-ibdsav - 1, lowerDifference.getEntry(-ibdsav - 1));<a name="line.1421"></a>
<FONT color="green">1422</FONT>            }<a name="line.1422"></a>
<FONT color="green">1423</FONT>            if (ibdsav &gt; 0) {<a name="line.1423"></a>
<FONT color="green">1424</FONT>                newPoint.setEntry(ibdsav - 1, upperDifference.getEntry(ibdsav - 1));<a name="line.1424"></a>
<FONT color="green">1425</FONT>            }<a name="line.1425"></a>
<FONT color="green">1426</FONT>    <a name="line.1426"></a>
<FONT color="green">1427</FONT>            // Prepare for the iterative method that assembles the constrained Cauchy<a name="line.1427"></a>
<FONT color="green">1428</FONT>            // step in W. The sum of squares of the fixed components of W is formed in<a name="line.1428"></a>
<FONT color="green">1429</FONT>            // WFIXSQ, and the free components of W are set to BIGSTP.<a name="line.1429"></a>
<FONT color="green">1430</FONT>    <a name="line.1430"></a>
<FONT color="green">1431</FONT>            final double bigstp = adelt + adelt;<a name="line.1431"></a>
<FONT color="green">1432</FONT>            int iflag = 0;<a name="line.1432"></a>
<FONT color="green">1433</FONT>            double cauchy = Double.NaN;<a name="line.1433"></a>
<FONT color="green">1434</FONT>            double csave = ZERO;<a name="line.1434"></a>
<FONT color="green">1435</FONT>            while (true) {<a name="line.1435"></a>
<FONT color="green">1436</FONT>                double wfixsq = ZERO;<a name="line.1436"></a>
<FONT color="green">1437</FONT>                double ggfree = ZERO;<a name="line.1437"></a>
<FONT color="green">1438</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.1438"></a>
<FONT color="green">1439</FONT>                    final double glagValue = glag.getEntry(i);<a name="line.1439"></a>
<FONT color="green">1440</FONT>                    work1.setEntry(i, ZERO);<a name="line.1440"></a>
<FONT color="green">1441</FONT>                    if (Math.min(trustRegionCenterOffset.getEntry(i) - lowerDifference.getEntry(i), glagValue) &gt; ZERO ||<a name="line.1441"></a>
<FONT color="green">1442</FONT>                        Math.max(trustRegionCenterOffset.getEntry(i) - upperDifference.getEntry(i), glagValue) &lt; ZERO) {<a name="line.1442"></a>
<FONT color="green">1443</FONT>                        work1.setEntry(i, bigstp);<a name="line.1443"></a>
<FONT color="green">1444</FONT>                        // Computing 2nd power<a name="line.1444"></a>
<FONT color="green">1445</FONT>                        ggfree += glagValue * glagValue;<a name="line.1445"></a>
<FONT color="green">1446</FONT>                    }<a name="line.1446"></a>
<FONT color="green">1447</FONT>                }<a name="line.1447"></a>
<FONT color="green">1448</FONT>                if (ggfree == ZERO) {<a name="line.1448"></a>
<FONT color="green">1449</FONT>                    return new double[] { alpha, ZERO };<a name="line.1449"></a>
<FONT color="green">1450</FONT>                }<a name="line.1450"></a>
<FONT color="green">1451</FONT>    <a name="line.1451"></a>
<FONT color="green">1452</FONT>                // Investigate whether more components of W can be fixed.<a name="line.1452"></a>
<FONT color="green">1453</FONT>                final double tmp1 = adelt * adelt - wfixsq;<a name="line.1453"></a>
<FONT color="green">1454</FONT>                if (tmp1 &gt; ZERO) {<a name="line.1454"></a>
<FONT color="green">1455</FONT>                    step = Math.sqrt(tmp1 / ggfree);<a name="line.1455"></a>
<FONT color="green">1456</FONT>                    ggfree = ZERO;<a name="line.1456"></a>
<FONT color="green">1457</FONT>                    for (int i = 0; i &lt; n; i++) {<a name="line.1457"></a>
<FONT color="green">1458</FONT>                        if (work1.getEntry(i) == bigstp) {<a name="line.1458"></a>
<FONT color="green">1459</FONT>                            final double tmp2 = trustRegionCenterOffset.getEntry(i) - step * glag.getEntry(i);<a name="line.1459"></a>
<FONT color="green">1460</FONT>                            if (tmp2 &lt;= lowerDifference.getEntry(i)) {<a name="line.1460"></a>
<FONT color="green">1461</FONT>                                work1.setEntry(i, lowerDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i));<a name="line.1461"></a>
<FONT color="green">1462</FONT>                                // Computing 2nd power<a name="line.1462"></a>
<FONT color="green">1463</FONT>                                final double d1 = work1.getEntry(i);<a name="line.1463"></a>
<FONT color="green">1464</FONT>                                wfixsq += d1 * d1;<a name="line.1464"></a>
<FONT color="green">1465</FONT>                            } else if (tmp2 &gt;= upperDifference.getEntry(i)) {<a name="line.1465"></a>
<FONT color="green">1466</FONT>                                work1.setEntry(i, upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i));<a name="line.1466"></a>
<FONT color="green">1467</FONT>                                // Computing 2nd power<a name="line.1467"></a>
<FONT color="green">1468</FONT>                                final double d1 = work1.getEntry(i);<a name="line.1468"></a>
<FONT color="green">1469</FONT>                                wfixsq += d1 * d1;<a name="line.1469"></a>
<FONT color="green">1470</FONT>                            } else {<a name="line.1470"></a>
<FONT color="green">1471</FONT>                                // Computing 2nd power<a name="line.1471"></a>
<FONT color="green">1472</FONT>                                final double d1 = glag.getEntry(i);<a name="line.1472"></a>
<FONT color="green">1473</FONT>                                ggfree += d1 * d1;<a name="line.1473"></a>
<FONT color="green">1474</FONT>                            }<a name="line.1474"></a>
<FONT color="green">1475</FONT>                        }<a name="line.1475"></a>
<FONT color="green">1476</FONT>                    }<a name="line.1476"></a>
<FONT color="green">1477</FONT>                }<a name="line.1477"></a>
<FONT color="green">1478</FONT>    <a name="line.1478"></a>
<FONT color="green">1479</FONT>                // Set the remaining free components of W and all components of XALT,<a name="line.1479"></a>
<FONT color="green">1480</FONT>                // except that W may be scaled later.<a name="line.1480"></a>
<FONT color="green">1481</FONT>    <a name="line.1481"></a>
<FONT color="green">1482</FONT>                double gw = ZERO;<a name="line.1482"></a>
<FONT color="green">1483</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.1483"></a>
<FONT color="green">1484</FONT>                    final double glagValue = glag.getEntry(i);<a name="line.1484"></a>
<FONT color="green">1485</FONT>                    if (work1.getEntry(i) == bigstp) {<a name="line.1485"></a>
<FONT color="green">1486</FONT>                        work1.setEntry(i, -step * glagValue);<a name="line.1486"></a>
<FONT color="green">1487</FONT>                        final double min = Math.min(upperDifference.getEntry(i),<a name="line.1487"></a>
<FONT color="green">1488</FONT>                                                    trustRegionCenterOffset.getEntry(i) + work1.getEntry(i));<a name="line.1488"></a>
<FONT color="green">1489</FONT>                        alternativeNewPoint.setEntry(i, Math.max(lowerDifference.getEntry(i), min));<a name="line.1489"></a>
<FONT color="green">1490</FONT>                    } else if (work1.getEntry(i) == ZERO) {<a name="line.1490"></a>
<FONT color="green">1491</FONT>                        alternativeNewPoint.setEntry(i, trustRegionCenterOffset.getEntry(i));<a name="line.1491"></a>
<FONT color="green">1492</FONT>                    } else if (glagValue &gt; ZERO) {<a name="line.1492"></a>
<FONT color="green">1493</FONT>                        alternativeNewPoint.setEntry(i, lowerDifference.getEntry(i));<a name="line.1493"></a>
<FONT color="green">1494</FONT>                    } else {<a name="line.1494"></a>
<FONT color="green">1495</FONT>                        alternativeNewPoint.setEntry(i, upperDifference.getEntry(i));<a name="line.1495"></a>
<FONT color="green">1496</FONT>                    }<a name="line.1496"></a>
<FONT color="green">1497</FONT>                    gw += glagValue * work1.getEntry(i);<a name="line.1497"></a>
<FONT color="green">1498</FONT>                }<a name="line.1498"></a>
<FONT color="green">1499</FONT>    <a name="line.1499"></a>
<FONT color="green">1500</FONT>                // Set CURV to the curvature of the KNEW-th Lagrange function along W.<a name="line.1500"></a>
<FONT color="green">1501</FONT>                // Scale W by a factor less than one if that can reduce the modulus of<a name="line.1501"></a>
<FONT color="green">1502</FONT>                // the Lagrange function at XOPT+W. Set CAUCHY to the final value of<a name="line.1502"></a>
<FONT color="green">1503</FONT>                // the square of this function.<a name="line.1503"></a>
<FONT color="green">1504</FONT>    <a name="line.1504"></a>
<FONT color="green">1505</FONT>                double curv = ZERO;<a name="line.1505"></a>
<FONT color="green">1506</FONT>                for (int k = 0; k &lt; npt; k++) {<a name="line.1506"></a>
<FONT color="green">1507</FONT>                    double tmp = ZERO;<a name="line.1507"></a>
<FONT color="green">1508</FONT>                    for (int j = 0; j &lt; n; j++) {<a name="line.1508"></a>
<FONT color="green">1509</FONT>                        tmp += interpolationPoints.getEntry(k, j) * work1.getEntry(j);<a name="line.1509"></a>
<FONT color="green">1510</FONT>                    }<a name="line.1510"></a>
<FONT color="green">1511</FONT>                    curv += hcol.getEntry(k) * tmp * tmp;<a name="line.1511"></a>
<FONT color="green">1512</FONT>                }<a name="line.1512"></a>
<FONT color="green">1513</FONT>                if (iflag == 1) {<a name="line.1513"></a>
<FONT color="green">1514</FONT>                    curv = -curv;<a name="line.1514"></a>
<FONT color="green">1515</FONT>                }<a name="line.1515"></a>
<FONT color="green">1516</FONT>                if (curv &gt; -gw &amp;&amp;<a name="line.1516"></a>
<FONT color="green">1517</FONT>                    curv &lt; -gw * (ONE + Math.sqrt(TWO))) {<a name="line.1517"></a>
<FONT color="green">1518</FONT>                    final double scale = -gw / curv;<a name="line.1518"></a>
<FONT color="green">1519</FONT>                    for (int i = 0; i &lt; n; i++) {<a name="line.1519"></a>
<FONT color="green">1520</FONT>                        final double tmp = trustRegionCenterOffset.getEntry(i) + scale * work1.getEntry(i);<a name="line.1520"></a>
<FONT color="green">1521</FONT>                        alternativeNewPoint.setEntry(i, Math.max(lowerDifference.getEntry(i),<a name="line.1521"></a>
<FONT color="green">1522</FONT>                                                  Math.min(upperDifference.getEntry(i), tmp)));<a name="line.1522"></a>
<FONT color="green">1523</FONT>                    }<a name="line.1523"></a>
<FONT color="green">1524</FONT>                    // Computing 2nd power<a name="line.1524"></a>
<FONT color="green">1525</FONT>                    final double d1 = HALF * gw * scale;<a name="line.1525"></a>
<FONT color="green">1526</FONT>                    cauchy = d1 * d1;<a name="line.1526"></a>
<FONT color="green">1527</FONT>                } else {<a name="line.1527"></a>
<FONT color="green">1528</FONT>                    // Computing 2nd power<a name="line.1528"></a>
<FONT color="green">1529</FONT>                    final double d1 = gw + HALF * curv;<a name="line.1529"></a>
<FONT color="green">1530</FONT>                    cauchy = d1 * d1;<a name="line.1530"></a>
<FONT color="green">1531</FONT>                }<a name="line.1531"></a>
<FONT color="green">1532</FONT>    <a name="line.1532"></a>
<FONT color="green">1533</FONT>                // If IFLAG is zero, then XALT is calculated as before after reversing<a name="line.1533"></a>
<FONT color="green">1534</FONT>                // the sign of GLAG. Thus two XALT vectors become available. The one that<a name="line.1534"></a>
<FONT color="green">1535</FONT>                // is chosen is the one that gives the larger value of CAUCHY.<a name="line.1535"></a>
<FONT color="green">1536</FONT>    <a name="line.1536"></a>
<FONT color="green">1537</FONT>                if (iflag == 0) {<a name="line.1537"></a>
<FONT color="green">1538</FONT>                    for (int i = 0; i &lt; n; i++) {<a name="line.1538"></a>
<FONT color="green">1539</FONT>                        glag.setEntry(i, -glag.getEntry(i));<a name="line.1539"></a>
<FONT color="green">1540</FONT>                        work2.setEntry(i, alternativeNewPoint.getEntry(i));<a name="line.1540"></a>
<FONT color="green">1541</FONT>                    }<a name="line.1541"></a>
<FONT color="green">1542</FONT>                    csave = cauchy;<a name="line.1542"></a>
<FONT color="green">1543</FONT>                    iflag = 1;<a name="line.1543"></a>
<FONT color="green">1544</FONT>                } else {<a name="line.1544"></a>
<FONT color="green">1545</FONT>                    break;<a name="line.1545"></a>
<FONT color="green">1546</FONT>                }<a name="line.1546"></a>
<FONT color="green">1547</FONT>            }<a name="line.1547"></a>
<FONT color="green">1548</FONT>            if (csave &gt; cauchy) {<a name="line.1548"></a>
<FONT color="green">1549</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.1549"></a>
<FONT color="green">1550</FONT>                    alternativeNewPoint.setEntry(i, work2.getEntry(i));<a name="line.1550"></a>
<FONT color="green">1551</FONT>                }<a name="line.1551"></a>
<FONT color="green">1552</FONT>                cauchy = csave;<a name="line.1552"></a>
<FONT color="green">1553</FONT>            }<a name="line.1553"></a>
<FONT color="green">1554</FONT>    <a name="line.1554"></a>
<FONT color="green">1555</FONT>            return new double[] { alpha, cauchy };<a name="line.1555"></a>
<FONT color="green">1556</FONT>        } // altmov<a name="line.1556"></a>
<FONT color="green">1557</FONT>    <a name="line.1557"></a>
<FONT color="green">1558</FONT>        // ----------------------------------------------------------------------------------------<a name="line.1558"></a>
<FONT color="green">1559</FONT>    <a name="line.1559"></a>
<FONT color="green">1560</FONT>        /**<a name="line.1560"></a>
<FONT color="green">1561</FONT>         *     SUBROUTINE PRELIM sets the elements of XBASE, XPT, FVAL, GOPT, HQ, PQ,<a name="line.1561"></a>
<FONT color="green">1562</FONT>         *     BMAT and ZMAT for the first iteration, and it maintains the values of<a name="line.1562"></a>
<FONT color="green">1563</FONT>         *     NF and KOPT. The vector X is also changed by PRELIM.<a name="line.1563"></a>
<FONT color="green">1564</FONT>         *<a name="line.1564"></a>
<FONT color="green">1565</FONT>         *     The arguments N, NPT, X, XL, XU, RHOBEG, IPRINT and MAXFUN are the<a name="line.1565"></a>
<FONT color="green">1566</FONT>         *       same as the corresponding arguments in SUBROUTINE BOBYQA.<a name="line.1566"></a>
<FONT color="green">1567</FONT>         *     The arguments XBASE, XPT, FVAL, HQ, PQ, BMAT, ZMAT, NDIM, SL and SU<a name="line.1567"></a>
<FONT color="green">1568</FONT>         *       are the same as the corresponding arguments in BOBYQB, the elements<a name="line.1568"></a>
<FONT color="green">1569</FONT>         *       of SL and SU being set in BOBYQA.<a name="line.1569"></a>
<FONT color="green">1570</FONT>         *     GOPT is usually the gradient of the quadratic model at XOPT+XBASE, but<a name="line.1570"></a>
<FONT color="green">1571</FONT>         *       it is set by PRELIM to the gradient of the quadratic model at XBASE.<a name="line.1571"></a>
<FONT color="green">1572</FONT>         *       If XOPT is nonzero, BOBYQB will change it to its usual value later.<a name="line.1572"></a>
<FONT color="green">1573</FONT>         *     NF is maintaned as the number of calls of CALFUN so far.<a name="line.1573"></a>
<FONT color="green">1574</FONT>         *     KOPT will be such that the least calculated value of F so far is at<a name="line.1574"></a>
<FONT color="green">1575</FONT>         *       the point XPT(KOPT,.)+XBASE in the space of the variables.<a name="line.1575"></a>
<FONT color="green">1576</FONT>         *<a name="line.1576"></a>
<FONT color="green">1577</FONT>         * @param lowerBound Lower bounds.<a name="line.1577"></a>
<FONT color="green">1578</FONT>         * @param upperBound Upper bounds.<a name="line.1578"></a>
<FONT color="green">1579</FONT>         */<a name="line.1579"></a>
<FONT color="green">1580</FONT>        private void prelim(double[] lowerBound,<a name="line.1580"></a>
<FONT color="green">1581</FONT>                            double[] upperBound) {<a name="line.1581"></a>
<FONT color="green">1582</FONT>            printMethod(); // XXX<a name="line.1582"></a>
<FONT color="green">1583</FONT>    <a name="line.1583"></a>
<FONT color="green">1584</FONT>            final int n = currentBest.getDimension();<a name="line.1584"></a>
<FONT color="green">1585</FONT>            final int npt = numberOfInterpolationPoints;<a name="line.1585"></a>
<FONT color="green">1586</FONT>            final int ndim = bMatrix.getRowDimension();<a name="line.1586"></a>
<FONT color="green">1587</FONT>    <a name="line.1587"></a>
<FONT color="green">1588</FONT>            final double rhosq = initialTrustRegionRadius * initialTrustRegionRadius;<a name="line.1588"></a>
<FONT color="green">1589</FONT>            final double recip = 1d / rhosq;<a name="line.1589"></a>
<FONT color="green">1590</FONT>            final int np = n + 1;<a name="line.1590"></a>
<FONT color="green">1591</FONT>    <a name="line.1591"></a>
<FONT color="green">1592</FONT>            // Set XBASE to the initial vector of variables, and set the initial<a name="line.1592"></a>
<FONT color="green">1593</FONT>            // elements of XPT, BMAT, HQ, PQ and ZMAT to zero.<a name="line.1593"></a>
<FONT color="green">1594</FONT>    <a name="line.1594"></a>
<FONT color="green">1595</FONT>            for (int j = 0; j &lt; n; j++) {<a name="line.1595"></a>
<FONT color="green">1596</FONT>                originShift.setEntry(j, currentBest.getEntry(j));<a name="line.1596"></a>
<FONT color="green">1597</FONT>                for (int k = 0; k &lt; npt; k++) {<a name="line.1597"></a>
<FONT color="green">1598</FONT>                    interpolationPoints.setEntry(k, j, ZERO);<a name="line.1598"></a>
<FONT color="green">1599</FONT>                }<a name="line.1599"></a>
<FONT color="green">1600</FONT>                for (int i = 0; i &lt; ndim; i++) {<a name="line.1600"></a>
<FONT color="green">1601</FONT>                    bMatrix.setEntry(i, j, ZERO);<a name="line.1601"></a>
<FONT color="green">1602</FONT>                }<a name="line.1602"></a>
<FONT color="green">1603</FONT>            }<a name="line.1603"></a>
<FONT color="green">1604</FONT>            for (int i = 0, max = n * np / 2; i &lt; max; i++) {<a name="line.1604"></a>
<FONT color="green">1605</FONT>                modelSecondDerivativesValues.setEntry(i, ZERO);<a name="line.1605"></a>
<FONT color="green">1606</FONT>            }<a name="line.1606"></a>
<FONT color="green">1607</FONT>            for (int k = 0; k &lt; npt; k++) {<a name="line.1607"></a>
<FONT color="green">1608</FONT>                modelSecondDerivativesParameters.setEntry(k, ZERO);<a name="line.1608"></a>
<FONT color="green">1609</FONT>                for (int j = 0, max = npt - np; j &lt; max; j++) {<a name="line.1609"></a>
<FONT color="green">1610</FONT>                    zMatrix.setEntry(k, j, ZERO);<a name="line.1610"></a>
<FONT color="green">1611</FONT>                }<a name="line.1611"></a>
<FONT color="green">1612</FONT>            }<a name="line.1612"></a>
<FONT color="green">1613</FONT>    <a name="line.1613"></a>
<FONT color="green">1614</FONT>            // Begin the initialization procedure. NF becomes one more than the number<a name="line.1614"></a>
<FONT color="green">1615</FONT>            // of function values so far. The coordinates of the displacement of the<a name="line.1615"></a>
<FONT color="green">1616</FONT>            // next initial interpolation point from XBASE are set in XPT(NF+1,.).<a name="line.1616"></a>
<FONT color="green">1617</FONT>    <a name="line.1617"></a>
<FONT color="green">1618</FONT>            int ipt = 0;<a name="line.1618"></a>
<FONT color="green">1619</FONT>            int jpt = 0;<a name="line.1619"></a>
<FONT color="green">1620</FONT>            double fbeg = Double.NaN;<a name="line.1620"></a>
<FONT color="green">1621</FONT>            do {<a name="line.1621"></a>
<FONT color="green">1622</FONT>                final int nfm = getEvaluations();<a name="line.1622"></a>
<FONT color="green">1623</FONT>                final int nfx = nfm - n;<a name="line.1623"></a>
<FONT color="green">1624</FONT>                final int nfmm = nfm - 1;<a name="line.1624"></a>
<FONT color="green">1625</FONT>                final int nfxm = nfx - 1;<a name="line.1625"></a>
<FONT color="green">1626</FONT>                double stepa = 0;<a name="line.1626"></a>
<FONT color="green">1627</FONT>                double stepb = 0;<a name="line.1627"></a>
<FONT color="green">1628</FONT>                if (nfm &lt;= 2 * n) {<a name="line.1628"></a>
<FONT color="green">1629</FONT>                    if (nfm &gt;= 1 &amp;&amp;<a name="line.1629"></a>
<FONT color="green">1630</FONT>                        nfm &lt;= n) {<a name="line.1630"></a>
<FONT color="green">1631</FONT>                        stepa = initialTrustRegionRadius;<a name="line.1631"></a>
<FONT color="green">1632</FONT>                        if (upperDifference.getEntry(nfmm) == ZERO) {<a name="line.1632"></a>
<FONT color="green">1633</FONT>                            stepa = -stepa;<a name="line.1633"></a>
<FONT color="green">1634</FONT>                            // throw new PathIsExploredException(); // XXX<a name="line.1634"></a>
<FONT color="green">1635</FONT>                        }<a name="line.1635"></a>
<FONT color="green">1636</FONT>                        interpolationPoints.setEntry(nfm, nfmm, stepa);<a name="line.1636"></a>
<FONT color="green">1637</FONT>                    } else if (nfm &gt; n) {<a name="line.1637"></a>
<FONT color="green">1638</FONT>                        stepa = interpolationPoints.getEntry(nfx, nfxm);<a name="line.1638"></a>
<FONT color="green">1639</FONT>                        stepb = -initialTrustRegionRadius;<a name="line.1639"></a>
<FONT color="green">1640</FONT>                        if (lowerDifference.getEntry(nfxm) == ZERO) {<a name="line.1640"></a>
<FONT color="green">1641</FONT>                            stepb = Math.min(TWO * initialTrustRegionRadius, upperDifference.getEntry(nfxm));<a name="line.1641"></a>
<FONT color="green">1642</FONT>                            // throw new PathIsExploredException(); // XXX<a name="line.1642"></a>
<FONT color="green">1643</FONT>                        }<a name="line.1643"></a>
<FONT color="green">1644</FONT>                        if (upperDifference.getEntry(nfxm) == ZERO) {<a name="line.1644"></a>
<FONT color="green">1645</FONT>                            stepb = Math.max(-TWO * initialTrustRegionRadius, lowerDifference.getEntry(nfxm));<a name="line.1645"></a>
<FONT color="green">1646</FONT>                            // throw new PathIsExploredException(); // XXX<a name="line.1646"></a>
<FONT color="green">1647</FONT>                        }<a name="line.1647"></a>
<FONT color="green">1648</FONT>                        interpolationPoints.setEntry(nfm, nfxm, stepb);<a name="line.1648"></a>
<FONT color="green">1649</FONT>                    }<a name="line.1649"></a>
<FONT color="green">1650</FONT>                } else {<a name="line.1650"></a>
<FONT color="green">1651</FONT>                    final int tmp1 = (nfm - np) / n;<a name="line.1651"></a>
<FONT color="green">1652</FONT>                    jpt = nfm - tmp1 * n - n;<a name="line.1652"></a>
<FONT color="green">1653</FONT>                    ipt = jpt + tmp1;<a name="line.1653"></a>
<FONT color="green">1654</FONT>                    if (ipt &gt; n) {<a name="line.1654"></a>
<FONT color="green">1655</FONT>                        final int tmp2 = jpt;<a name="line.1655"></a>
<FONT color="green">1656</FONT>                        jpt = ipt - n;<a name="line.1656"></a>
<FONT color="green">1657</FONT>                        ipt = tmp2;<a name="line.1657"></a>
<FONT color="green">1658</FONT>    //                     throw new PathIsExploredException(); // XXX<a name="line.1658"></a>
<FONT color="green">1659</FONT>                    }<a name="line.1659"></a>
<FONT color="green">1660</FONT>                    final int iptMinus1 = ipt - 1;<a name="line.1660"></a>
<FONT color="green">1661</FONT>                    final int jptMinus1 = jpt - 1;<a name="line.1661"></a>
<FONT color="green">1662</FONT>                    interpolationPoints.setEntry(nfm, iptMinus1, interpolationPoints.getEntry(ipt, iptMinus1));<a name="line.1662"></a>
<FONT color="green">1663</FONT>                    interpolationPoints.setEntry(nfm, jptMinus1, interpolationPoints.getEntry(jpt, jptMinus1));<a name="line.1663"></a>
<FONT color="green">1664</FONT>                }<a name="line.1664"></a>
<FONT color="green">1665</FONT>    <a name="line.1665"></a>
<FONT color="green">1666</FONT>                // Calculate the next value of F. The least function value so far and<a name="line.1666"></a>
<FONT color="green">1667</FONT>                // its index are required.<a name="line.1667"></a>
<FONT color="green">1668</FONT>    <a name="line.1668"></a>
<FONT color="green">1669</FONT>                for (int j = 0; j &lt; n; j++) {<a name="line.1669"></a>
<FONT color="green">1670</FONT>                    currentBest.setEntry(j, Math.min(Math.max(lowerBound[j],<a name="line.1670"></a>
<FONT color="green">1671</FONT>                                                              originShift.getEntry(j) + interpolationPoints.getEntry(nfm, j)),<a name="line.1671"></a>
<FONT color="green">1672</FONT>                                                     upperBound[j]));<a name="line.1672"></a>
<FONT color="green">1673</FONT>                    if (interpolationPoints.getEntry(nfm, j) == lowerDifference.getEntry(j)) {<a name="line.1673"></a>
<FONT color="green">1674</FONT>                        currentBest.setEntry(j, lowerBound[j]);<a name="line.1674"></a>
<FONT color="green">1675</FONT>                    }<a name="line.1675"></a>
<FONT color="green">1676</FONT>                    if (interpolationPoints.getEntry(nfm, j) == upperDifference.getEntry(j)) {<a name="line.1676"></a>
<FONT color="green">1677</FONT>                        currentBest.setEntry(j, upperBound[j]);<a name="line.1677"></a>
<FONT color="green">1678</FONT>                    }<a name="line.1678"></a>
<FONT color="green">1679</FONT>                }<a name="line.1679"></a>
<FONT color="green">1680</FONT>    <a name="line.1680"></a>
<FONT color="green">1681</FONT>                final double objectiveValue = computeObjectiveValue(currentBest.toArray());<a name="line.1681"></a>
<FONT color="green">1682</FONT>                final double f = isMinimize ? objectiveValue : -objectiveValue;<a name="line.1682"></a>
<FONT color="green">1683</FONT>                final int numEval = getEvaluations(); // nfm + 1<a name="line.1683"></a>
<FONT color="green">1684</FONT>                fAtInterpolationPoints.setEntry(nfm, f);<a name="line.1684"></a>
<FONT color="green">1685</FONT>    <a name="line.1685"></a>
<FONT color="green">1686</FONT>                if (numEval == 1) {<a name="line.1686"></a>
<FONT color="green">1687</FONT>                    fbeg = f;<a name="line.1687"></a>
<FONT color="green">1688</FONT>                    trustRegionCenterInterpolationPointIndex = 0;<a name="line.1688"></a>
<FONT color="green">1689</FONT>                } else if (f &lt; fAtInterpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex)) {<a name="line.1689"></a>
<FONT color="green">1690</FONT>                    trustRegionCenterInterpolationPointIndex = nfm;<a name="line.1690"></a>
<FONT color="green">1691</FONT>                }<a name="line.1691"></a>
<FONT color="green">1692</FONT>    <a name="line.1692"></a>
<FONT color="green">1693</FONT>                // Set the nonzero initial elements of BMAT and the quadratic model in the<a name="line.1693"></a>
<FONT color="green">1694</FONT>                // cases when NF is at most 2*N+1. If NF exceeds N+1, then the positions<a name="line.1694"></a>
<FONT color="green">1695</FONT>                // of the NF-th and (NF-N)-th interpolation points may be switched, in<a name="line.1695"></a>
<FONT color="green">1696</FONT>                // order that the function value at the first of them contributes to the<a name="line.1696"></a>
<FONT color="green">1697</FONT>                // off-diagonal second derivative terms of the initial quadratic model.<a name="line.1697"></a>
<FONT color="green">1698</FONT>    <a name="line.1698"></a>
<FONT color="green">1699</FONT>                if (numEval &lt;= 2 * n + 1) {<a name="line.1699"></a>
<FONT color="green">1700</FONT>                    if (numEval &gt;= 2 &amp;&amp;<a name="line.1700"></a>
<FONT color="green">1701</FONT>                        numEval &lt;= n + 1) {<a name="line.1701"></a>
<FONT color="green">1702</FONT>                        gradientAtTrustRegionCenter.setEntry(nfmm, (f - fbeg) / stepa);<a name="line.1702"></a>
<FONT color="green">1703</FONT>                        if (npt &lt; numEval + n) {<a name="line.1703"></a>
<FONT color="green">1704</FONT>                            final double oneOverStepA = ONE / stepa;<a name="line.1704"></a>
<FONT color="green">1705</FONT>                            bMatrix.setEntry(0, nfmm, -oneOverStepA);<a name="line.1705"></a>
<FONT color="green">1706</FONT>                            bMatrix.setEntry(nfm, nfmm, oneOverStepA);<a name="line.1706"></a>
<FONT color="green">1707</FONT>                            bMatrix.setEntry(npt + nfmm, nfmm, -HALF * rhosq);<a name="line.1707"></a>
<FONT color="green">1708</FONT>                            // throw new PathIsExploredException(); // XXX<a name="line.1708"></a>
<FONT color="green">1709</FONT>                        }<a name="line.1709"></a>
<FONT color="green">1710</FONT>                    } else if (numEval &gt;= n + 2) {<a name="line.1710"></a>
<FONT color="green">1711</FONT>                        final int ih = nfx * (nfx + 1) / 2 - 1;<a name="line.1711"></a>
<FONT color="green">1712</FONT>                        final double tmp = (f - fbeg) / stepb;<a name="line.1712"></a>
<FONT color="green">1713</FONT>                        final double diff = stepb - stepa;<a name="line.1713"></a>
<FONT color="green">1714</FONT>                        modelSecondDerivativesValues.setEntry(ih, TWO * (tmp - gradientAtTrustRegionCenter.getEntry(nfxm)) / diff);<a name="line.1714"></a>
<FONT color="green">1715</FONT>                        gradientAtTrustRegionCenter.setEntry(nfxm, (gradientAtTrustRegionCenter.getEntry(nfxm) * stepb - tmp * stepa) / diff);<a name="line.1715"></a>
<FONT color="green">1716</FONT>                        if (stepa * stepb &lt; ZERO) {<a name="line.1716"></a>
<FONT color="green">1717</FONT>                            if (f &lt; fAtInterpolationPoints.getEntry(nfm - n)) {<a name="line.1717"></a>
<FONT color="green">1718</FONT>                                fAtInterpolationPoints.setEntry(nfm, fAtInterpolationPoints.getEntry(nfm - n));<a name="line.1718"></a>
<FONT color="green">1719</FONT>                                fAtInterpolationPoints.setEntry(nfm - n, f);<a name="line.1719"></a>
<FONT color="green">1720</FONT>                                if (trustRegionCenterInterpolationPointIndex == nfm) {<a name="line.1720"></a>
<FONT color="green">1721</FONT>                                    trustRegionCenterInterpolationPointIndex = nfm - n;<a name="line.1721"></a>
<FONT color="green">1722</FONT>                                }<a name="line.1722"></a>
<FONT color="green">1723</FONT>                                interpolationPoints.setEntry(nfm - n, nfxm, stepb);<a name="line.1723"></a>
<FONT color="green">1724</FONT>                                interpolationPoints.setEntry(nfm, nfxm, stepa);<a name="line.1724"></a>
<FONT color="green">1725</FONT>                            }<a name="line.1725"></a>
<FONT color="green">1726</FONT>                        }<a name="line.1726"></a>
<FONT color="green">1727</FONT>                        bMatrix.setEntry(0, nfxm, -(stepa + stepb) / (stepa * stepb));<a name="line.1727"></a>
<FONT color="green">1728</FONT>                        bMatrix.setEntry(nfm, nfxm, -HALF / interpolationPoints.getEntry(nfm - n, nfxm));<a name="line.1728"></a>
<FONT color="green">1729</FONT>                        bMatrix.setEntry(nfm - n, nfxm,<a name="line.1729"></a>
<FONT color="green">1730</FONT>                                      -bMatrix.getEntry(0, nfxm) - bMatrix.getEntry(nfm, nfxm));<a name="line.1730"></a>
<FONT color="green">1731</FONT>                        zMatrix.setEntry(0, nfxm, Math.sqrt(TWO) / (stepa * stepb));<a name="line.1731"></a>
<FONT color="green">1732</FONT>                        zMatrix.setEntry(nfm, nfxm, Math.sqrt(HALF) / rhosq);<a name="line.1732"></a>
<FONT color="green">1733</FONT>                        // zMatrix.setEntry(nfm, nfxm, Math.sqrt(HALF) * recip); // XXX "testAckley" and "testDiffPow" fail.<a name="line.1733"></a>
<FONT color="green">1734</FONT>                        zMatrix.setEntry(nfm - n, nfxm,<a name="line.1734"></a>
<FONT color="green">1735</FONT>                                      -zMatrix.getEntry(0, nfxm) - zMatrix.getEntry(nfm, nfxm));<a name="line.1735"></a>
<FONT color="green">1736</FONT>                    }<a name="line.1736"></a>
<FONT color="green">1737</FONT>    <a name="line.1737"></a>
<FONT color="green">1738</FONT>                    // Set the off-diagonal second derivatives of the Lagrange functions and<a name="line.1738"></a>
<FONT color="green">1739</FONT>                    // the initial quadratic model.<a name="line.1739"></a>
<FONT color="green">1740</FONT>    <a name="line.1740"></a>
<FONT color="green">1741</FONT>                } else {<a name="line.1741"></a>
<FONT color="green">1742</FONT>                    zMatrix.setEntry(0, nfxm, recip);<a name="line.1742"></a>
<FONT color="green">1743</FONT>                    zMatrix.setEntry(nfm, nfxm, recip);<a name="line.1743"></a>
<FONT color="green">1744</FONT>                    zMatrix.setEntry(ipt, nfxm, -recip);<a name="line.1744"></a>
<FONT color="green">1745</FONT>                    zMatrix.setEntry(jpt, nfxm, -recip);<a name="line.1745"></a>
<FONT color="green">1746</FONT>    <a name="line.1746"></a>
<FONT color="green">1747</FONT>                    final int ih = ipt * (ipt - 1) / 2 + jpt - 1;<a name="line.1747"></a>
<FONT color="green">1748</FONT>                    final double tmp = interpolationPoints.getEntry(nfm, ipt - 1) * interpolationPoints.getEntry(nfm, jpt - 1);<a name="line.1748"></a>
<FONT color="green">1749</FONT>                    modelSecondDerivativesValues.setEntry(ih, (fbeg - fAtInterpolationPoints.getEntry(ipt) - fAtInterpolationPoints.getEntry(jpt) + f) / tmp);<a name="line.1749"></a>
<FONT color="green">1750</FONT>    //                 throw new PathIsExploredException(); // XXX<a name="line.1750"></a>
<FONT color="green">1751</FONT>                }<a name="line.1751"></a>
<FONT color="green">1752</FONT>            } while (getEvaluations() &lt; npt);<a name="line.1752"></a>
<FONT color="green">1753</FONT>        } // prelim<a name="line.1753"></a>
<FONT color="green">1754</FONT>    <a name="line.1754"></a>
<FONT color="green">1755</FONT>    <a name="line.1755"></a>
<FONT color="green">1756</FONT>        // ----------------------------------------------------------------------------------------<a name="line.1756"></a>
<FONT color="green">1757</FONT>    <a name="line.1757"></a>
<FONT color="green">1758</FONT>        /**<a name="line.1758"></a>
<FONT color="green">1759</FONT>         *     A version of the truncated conjugate gradient is applied. If a line<a name="line.1759"></a>
<FONT color="green">1760</FONT>         *     search is restricted by a constraint, then the procedure is restarted,<a name="line.1760"></a>
<FONT color="green">1761</FONT>         *     the values of the variables that are at their bounds being fixed. If<a name="line.1761"></a>
<FONT color="green">1762</FONT>         *     the trust region boundary is reached, then further changes may be made<a name="line.1762"></a>
<FONT color="green">1763</FONT>         *     to D, each one being in the two dimensional space that is spanned<a name="line.1763"></a>
<FONT color="green">1764</FONT>         *     by the current D and the gradient of Q at XOPT+D, staying on the trust<a name="line.1764"></a>
<FONT color="green">1765</FONT>         *     region boundary. Termination occurs when the reduction in Q seems to<a name="line.1765"></a>
<FONT color="green">1766</FONT>         *     be close to the greatest reduction that can be achieved.<a name="line.1766"></a>
<FONT color="green">1767</FONT>         *     The arguments N, NPT, XPT, XOPT, GOPT, HQ, PQ, SL and SU have the same<a name="line.1767"></a>
<FONT color="green">1768</FONT>         *       meanings as the corresponding arguments of BOBYQB.<a name="line.1768"></a>
<FONT color="green">1769</FONT>         *     DELTA is the trust region radius for the present calculation, which<a name="line.1769"></a>
<FONT color="green">1770</FONT>         *       seeks a small value of the quadratic model within distance DELTA of<a name="line.1770"></a>
<FONT color="green">1771</FONT>         *       XOPT subject to the bounds on the variables.<a name="line.1771"></a>
<FONT color="green">1772</FONT>         *     XNEW will be set to a new vector of variables that is approximately<a name="line.1772"></a>
<FONT color="green">1773</FONT>         *       the one that minimizes the quadratic model within the trust region<a name="line.1773"></a>
<FONT color="green">1774</FONT>         *       subject to the SL and SU constraints on the variables. It satisfies<a name="line.1774"></a>
<FONT color="green">1775</FONT>         *       as equations the bounds that become active during the calculation.<a name="line.1775"></a>
<FONT color="green">1776</FONT>         *     D is the calculated trial step from XOPT, generated iteratively from an<a name="line.1776"></a>
<FONT color="green">1777</FONT>         *       initial value of zero. Thus XNEW is XOPT+D after the final iteration.<a name="line.1777"></a>
<FONT color="green">1778</FONT>         *     GNEW holds the gradient of the quadratic model at XOPT+D. It is updated<a name="line.1778"></a>
<FONT color="green">1779</FONT>         *       when D is updated.<a name="line.1779"></a>
<FONT color="green">1780</FONT>         *     xbdi.get( is a working space vector. For I=1,2,...,N, the element xbdi.get((I) is<a name="line.1780"></a>
<FONT color="green">1781</FONT>         *       set to -1.0, 0.0, or 1.0, the value being nonzero if and only if the<a name="line.1781"></a>
<FONT color="green">1782</FONT>         *       I-th variable has become fixed at a bound, the bound being SL(I) or<a name="line.1782"></a>
<FONT color="green">1783</FONT>         *       SU(I) in the case xbdi.get((I)=-1.0 or xbdi.get((I)=1.0, respectively. This<a name="line.1783"></a>
<FONT color="green">1784</FONT>         *       information is accumulated during the construction of XNEW.<a name="line.1784"></a>
<FONT color="green">1785</FONT>         *     The arrays S, HS and HRED are also used for working space. They hold the<a name="line.1785"></a>
<FONT color="green">1786</FONT>         *       current search direction, and the changes in the gradient of Q along S<a name="line.1786"></a>
<FONT color="green">1787</FONT>         *       and the reduced D, respectively, where the reduced D is the same as D,<a name="line.1787"></a>
<FONT color="green">1788</FONT>         *       except that the components of the fixed variables are zero.<a name="line.1788"></a>
<FONT color="green">1789</FONT>         *     DSQ will be set to the square of the length of XNEW-XOPT.<a name="line.1789"></a>
<FONT color="green">1790</FONT>         *     CRVMIN is set to zero if D reaches the trust region boundary. Otherwise<a name="line.1790"></a>
<FONT color="green">1791</FONT>         *       it is set to the least curvature of H that occurs in the conjugate<a name="line.1791"></a>
<FONT color="green">1792</FONT>         *       gradient searches that are not restricted by any constraints. The<a name="line.1792"></a>
<FONT color="green">1793</FONT>         *       value CRVMIN=-1.0D0 is set, however, if all of these searches are<a name="line.1793"></a>
<FONT color="green">1794</FONT>         *       constrained.<a name="line.1794"></a>
<FONT color="green">1795</FONT>         * @param delta<a name="line.1795"></a>
<FONT color="green">1796</FONT>         * @param gnew<a name="line.1796"></a>
<FONT color="green">1797</FONT>         * @param xbdi<a name="line.1797"></a>
<FONT color="green">1798</FONT>         * @param s<a name="line.1798"></a>
<FONT color="green">1799</FONT>         * @param hs<a name="line.1799"></a>
<FONT color="green">1800</FONT>         * @param hred<a name="line.1800"></a>
<FONT color="green">1801</FONT>         */<a name="line.1801"></a>
<FONT color="green">1802</FONT>        private double[] trsbox(<a name="line.1802"></a>
<FONT color="green">1803</FONT>                double delta,<a name="line.1803"></a>
<FONT color="green">1804</FONT>                ArrayRealVector gnew,<a name="line.1804"></a>
<FONT color="green">1805</FONT>                ArrayRealVector xbdi,<a name="line.1805"></a>
<FONT color="green">1806</FONT>                ArrayRealVector s,<a name="line.1806"></a>
<FONT color="green">1807</FONT>                ArrayRealVector hs,<a name="line.1807"></a>
<FONT color="green">1808</FONT>                ArrayRealVector hred<a name="line.1808"></a>
<FONT color="green">1809</FONT>        ) {<a name="line.1809"></a>
<FONT color="green">1810</FONT>            printMethod(); // XXX<a name="line.1810"></a>
<FONT color="green">1811</FONT>    <a name="line.1811"></a>
<FONT color="green">1812</FONT>            final int n = currentBest.getDimension();<a name="line.1812"></a>
<FONT color="green">1813</FONT>            final int npt = numberOfInterpolationPoints;<a name="line.1813"></a>
<FONT color="green">1814</FONT>    <a name="line.1814"></a>
<FONT color="green">1815</FONT>            double dsq = Double.NaN;<a name="line.1815"></a>
<FONT color="green">1816</FONT>            double crvmin = Double.NaN;<a name="line.1816"></a>
<FONT color="green">1817</FONT>    <a name="line.1817"></a>
<FONT color="green">1818</FONT>            // Local variables<a name="line.1818"></a>
<FONT color="green">1819</FONT>            double ds;<a name="line.1819"></a>
<FONT color="green">1820</FONT>            int iu;<a name="line.1820"></a>
<FONT color="green">1821</FONT>            double dhd, dhs, cth, shs, sth, ssq, beta=0, sdec, blen;<a name="line.1821"></a>
<FONT color="green">1822</FONT>            int iact = -1;<a name="line.1822"></a>
<FONT color="green">1823</FONT>            int nact = 0;<a name="line.1823"></a>
<FONT color="green">1824</FONT>            double angt = 0, qred;<a name="line.1824"></a>
<FONT color="green">1825</FONT>            int isav;<a name="line.1825"></a>
<FONT color="green">1826</FONT>            double temp = 0, xsav = 0, xsum = 0, angbd = 0, dredg = 0, sredg = 0;<a name="line.1826"></a>
<FONT color="green">1827</FONT>            int iterc;<a name="line.1827"></a>
<FONT color="green">1828</FONT>            double resid = 0, delsq = 0, ggsav = 0, tempa = 0, tempb = 0,<a name="line.1828"></a>
<FONT color="green">1829</FONT>            redmax = 0, dredsq = 0, redsav = 0, gredsq = 0, rednew = 0;<a name="line.1829"></a>
<FONT color="green">1830</FONT>            int itcsav = 0;<a name="line.1830"></a>
<FONT color="green">1831</FONT>            double rdprev = 0, rdnext = 0, stplen = 0, stepsq = 0;<a name="line.1831"></a>
<FONT color="green">1832</FONT>            int itermax = 0;<a name="line.1832"></a>
<FONT color="green">1833</FONT>    <a name="line.1833"></a>
<FONT color="green">1834</FONT>            // Set some constants.<a name="line.1834"></a>
<FONT color="green">1835</FONT>    <a name="line.1835"></a>
<FONT color="green">1836</FONT>            // Function Body<a name="line.1836"></a>
<FONT color="green">1837</FONT>    <a name="line.1837"></a>
<FONT color="green">1838</FONT>            // The sign of GOPT(I) gives the sign of the change to the I-th variable<a name="line.1838"></a>
<FONT color="green">1839</FONT>            // that will reduce Q from its value at XOPT. Thus xbdi.get((I) shows whether<a name="line.1839"></a>
<FONT color="green">1840</FONT>            // or not to fix the I-th variable at one of its bounds initially, with<a name="line.1840"></a>
<FONT color="green">1841</FONT>            // NACT being set to the number of fixed variables. D and GNEW are also<a name="line.1841"></a>
<FONT color="green">1842</FONT>            // set for the first iteration. DELSQ is the upper bound on the sum of<a name="line.1842"></a>
<FONT color="green">1843</FONT>            // squares of the free variables. QRED is the reduction in Q so far.<a name="line.1843"></a>
<FONT color="green">1844</FONT>    <a name="line.1844"></a>
<FONT color="green">1845</FONT>            iterc = 0;<a name="line.1845"></a>
<FONT color="green">1846</FONT>            nact = 0;<a name="line.1846"></a>
<FONT color="green">1847</FONT>            for (int i = 0; i &lt; n; i++) {<a name="line.1847"></a>
<FONT color="green">1848</FONT>                xbdi.setEntry(i, ZERO);<a name="line.1848"></a>
<FONT color="green">1849</FONT>                if (trustRegionCenterOffset.getEntry(i) &lt;= lowerDifference.getEntry(i)) {<a name="line.1849"></a>
<FONT color="green">1850</FONT>                    if (gradientAtTrustRegionCenter.getEntry(i) &gt;= ZERO) {<a name="line.1850"></a>
<FONT color="green">1851</FONT>                        xbdi.setEntry(i, MINUS_ONE);<a name="line.1851"></a>
<FONT color="green">1852</FONT>                    }<a name="line.1852"></a>
<FONT color="green">1853</FONT>                } else if (trustRegionCenterOffset.getEntry(i) &gt;= upperDifference.getEntry(i)) {<a name="line.1853"></a>
<FONT color="green">1854</FONT>                    if (gradientAtTrustRegionCenter.getEntry(i) &lt;= ZERO) {<a name="line.1854"></a>
<FONT color="green">1855</FONT>                        xbdi.setEntry(i, ONE);<a name="line.1855"></a>
<FONT color="green">1856</FONT>                    }<a name="line.1856"></a>
<FONT color="green">1857</FONT>                }<a name="line.1857"></a>
<FONT color="green">1858</FONT>                if (xbdi.getEntry(i) != ZERO) {<a name="line.1858"></a>
<FONT color="green">1859</FONT>                    ++nact;<a name="line.1859"></a>
<FONT color="green">1860</FONT>                }<a name="line.1860"></a>
<FONT color="green">1861</FONT>                trialStepPoint.setEntry(i, ZERO);<a name="line.1861"></a>
<FONT color="green">1862</FONT>                gnew.setEntry(i, gradientAtTrustRegionCenter.getEntry(i));<a name="line.1862"></a>
<FONT color="green">1863</FONT>            }<a name="line.1863"></a>
<FONT color="green">1864</FONT>            delsq = delta * delta;<a name="line.1864"></a>
<FONT color="green">1865</FONT>            qred = ZERO;<a name="line.1865"></a>
<FONT color="green">1866</FONT>            crvmin = MINUS_ONE;<a name="line.1866"></a>
<FONT color="green">1867</FONT>    <a name="line.1867"></a>
<FONT color="green">1868</FONT>            // Set the next search direction of the conjugate gradient method. It is<a name="line.1868"></a>
<FONT color="green">1869</FONT>            // the steepest descent direction initially and when the iterations are<a name="line.1869"></a>
<FONT color="green">1870</FONT>            // restarted because a variable has just been fixed by a bound, and of<a name="line.1870"></a>
<FONT color="green">1871</FONT>            // course the components of the fixed variables are zero. ITERMAX is an<a name="line.1871"></a>
<FONT color="green">1872</FONT>            // upper bound on the indices of the conjugate gradient iterations.<a name="line.1872"></a>
<FONT color="green">1873</FONT>    <a name="line.1873"></a>
<FONT color="green">1874</FONT>            int state = 20;<a name="line.1874"></a>
<FONT color="green">1875</FONT>            for(;;) {<a name="line.1875"></a>
<FONT color="green">1876</FONT>                switch (state) {<a name="line.1876"></a>
<FONT color="green">1877</FONT>            case 20: {<a name="line.1877"></a>
<FONT color="green">1878</FONT>                printState(20); // XXX<a name="line.1878"></a>
<FONT color="green">1879</FONT>                beta = ZERO;<a name="line.1879"></a>
<FONT color="green">1880</FONT>            }<a name="line.1880"></a>
<FONT color="green">1881</FONT>            case 30: {<a name="line.1881"></a>
<FONT color="green">1882</FONT>                printState(30); // XXX<a name="line.1882"></a>
<FONT color="green">1883</FONT>                stepsq = ZERO;<a name="line.1883"></a>
<FONT color="green">1884</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.1884"></a>
<FONT color="green">1885</FONT>                    if (xbdi.getEntry(i) != ZERO) {<a name="line.1885"></a>
<FONT color="green">1886</FONT>                        s.setEntry(i, ZERO);<a name="line.1886"></a>
<FONT color="green">1887</FONT>                    } else if (beta == ZERO) {<a name="line.1887"></a>
<FONT color="green">1888</FONT>                        s.setEntry(i, -gnew.getEntry(i));<a name="line.1888"></a>
<FONT color="green">1889</FONT>                    } else {<a name="line.1889"></a>
<FONT color="green">1890</FONT>                        s.setEntry(i, beta * s.getEntry(i) - gnew.getEntry(i));<a name="line.1890"></a>
<FONT color="green">1891</FONT>                    }<a name="line.1891"></a>
<FONT color="green">1892</FONT>                    // Computing 2nd power<a name="line.1892"></a>
<FONT color="green">1893</FONT>                    final double d1 = s.getEntry(i);<a name="line.1893"></a>
<FONT color="green">1894</FONT>                    stepsq += d1 * d1;<a name="line.1894"></a>
<FONT color="green">1895</FONT>                }<a name="line.1895"></a>
<FONT color="green">1896</FONT>                if (stepsq == ZERO) {<a name="line.1896"></a>
<FONT color="green">1897</FONT>                    state = 190; break;<a name="line.1897"></a>
<FONT color="green">1898</FONT>                }<a name="line.1898"></a>
<FONT color="green">1899</FONT>                if (beta == ZERO) {<a name="line.1899"></a>
<FONT color="green">1900</FONT>                    gredsq = stepsq;<a name="line.1900"></a>
<FONT color="green">1901</FONT>                    itermax = iterc + n - nact;<a name="line.1901"></a>
<FONT color="green">1902</FONT>                }<a name="line.1902"></a>
<FONT color="green">1903</FONT>                if (gredsq * delsq &lt;= qred * 1e-4 * qred) {<a name="line.1903"></a>
<FONT color="green">1904</FONT>                    state = 190; break;<a name="line.1904"></a>
<FONT color="green">1905</FONT>                }<a name="line.1905"></a>
<FONT color="green">1906</FONT>    <a name="line.1906"></a>
<FONT color="green">1907</FONT>                // Multiply the search direction by the second derivative matrix of Q and<a name="line.1907"></a>
<FONT color="green">1908</FONT>                // calculate some scalars for the choice of steplength. Then set BLEN to<a name="line.1908"></a>
<FONT color="green">1909</FONT>                // the length of the the step to the trust region boundary and STPLEN to<a name="line.1909"></a>
<FONT color="green">1910</FONT>                // the steplength, ignoring the simple bounds.<a name="line.1910"></a>
<FONT color="green">1911</FONT>    <a name="line.1911"></a>
<FONT color="green">1912</FONT>                state = 210; break;<a name="line.1912"></a>
<FONT color="green">1913</FONT>            }<a name="line.1913"></a>
<FONT color="green">1914</FONT>            case 50: {<a name="line.1914"></a>
<FONT color="green">1915</FONT>                printState(50); // XXX<a name="line.1915"></a>
<FONT color="green">1916</FONT>                resid = delsq;<a name="line.1916"></a>
<FONT color="green">1917</FONT>                ds = ZERO;<a name="line.1917"></a>
<FONT color="green">1918</FONT>                shs = ZERO;<a name="line.1918"></a>
<FONT color="green">1919</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.1919"></a>
<FONT color="green">1920</FONT>                    if (xbdi.getEntry(i) == ZERO) {<a name="line.1920"></a>
<FONT color="green">1921</FONT>                        // Computing 2nd power<a name="line.1921"></a>
<FONT color="green">1922</FONT>                        final double d1 = trialStepPoint.getEntry(i);<a name="line.1922"></a>
<FONT color="green">1923</FONT>                        resid -= d1 * d1;<a name="line.1923"></a>
<FONT color="green">1924</FONT>                        ds += s.getEntry(i) * trialStepPoint.getEntry(i);<a name="line.1924"></a>
<FONT color="green">1925</FONT>                        shs += s.getEntry(i) * hs.getEntry(i);<a name="line.1925"></a>
<FONT color="green">1926</FONT>                    }<a name="line.1926"></a>
<FONT color="green">1927</FONT>                }<a name="line.1927"></a>
<FONT color="green">1928</FONT>                if (resid &lt;= ZERO) {<a name="line.1928"></a>
<FONT color="green">1929</FONT>                    state = 90; break;<a name="line.1929"></a>
<FONT color="green">1930</FONT>                }<a name="line.1930"></a>
<FONT color="green">1931</FONT>                temp = Math.sqrt(stepsq * resid + ds * ds);<a name="line.1931"></a>
<FONT color="green">1932</FONT>                if (ds &lt; ZERO) {<a name="line.1932"></a>
<FONT color="green">1933</FONT>                    blen = (temp - ds) / stepsq;<a name="line.1933"></a>
<FONT color="green">1934</FONT>                } else {<a name="line.1934"></a>
<FONT color="green">1935</FONT>                    blen = resid / (temp + ds);<a name="line.1935"></a>
<FONT color="green">1936</FONT>                }<a name="line.1936"></a>
<FONT color="green">1937</FONT>                stplen = blen;<a name="line.1937"></a>
<FONT color="green">1938</FONT>                if (shs &gt; ZERO) {<a name="line.1938"></a>
<FONT color="green">1939</FONT>                    // Computing MIN<a name="line.1939"></a>
<FONT color="green">1940</FONT>                    stplen = Math.min(blen, gredsq / shs);<a name="line.1940"></a>
<FONT color="green">1941</FONT>                }<a name="line.1941"></a>
<FONT color="green">1942</FONT>    <a name="line.1942"></a>
<FONT color="green">1943</FONT>                // Reduce STPLEN if necessary in order to preserve the simple bounds,<a name="line.1943"></a>
<FONT color="green">1944</FONT>                // letting IACT be the index of the new constrained variable.<a name="line.1944"></a>
<FONT color="green">1945</FONT>    <a name="line.1945"></a>
<FONT color="green">1946</FONT>                iact = -1;<a name="line.1946"></a>
<FONT color="green">1947</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.1947"></a>
<FONT color="green">1948</FONT>                    if (s.getEntry(i) != ZERO) {<a name="line.1948"></a>
<FONT color="green">1949</FONT>                        xsum = trustRegionCenterOffset.getEntry(i) + trialStepPoint.getEntry(i);<a name="line.1949"></a>
<FONT color="green">1950</FONT>                        if (s.getEntry(i) &gt; ZERO) {<a name="line.1950"></a>
<FONT color="green">1951</FONT>                            temp = (upperDifference.getEntry(i) - xsum) / s.getEntry(i);<a name="line.1951"></a>
<FONT color="green">1952</FONT>                        } else {<a name="line.1952"></a>
<FONT color="green">1953</FONT>                            temp = (lowerDifference.getEntry(i) - xsum) / s.getEntry(i);<a name="line.1953"></a>
<FONT color="green">1954</FONT>                        }<a name="line.1954"></a>
<FONT color="green">1955</FONT>                        if (temp &lt; stplen) {<a name="line.1955"></a>
<FONT color="green">1956</FONT>                            stplen = temp;<a name="line.1956"></a>
<FONT color="green">1957</FONT>                            iact = i;<a name="line.1957"></a>
<FONT color="green">1958</FONT>                        }<a name="line.1958"></a>
<FONT color="green">1959</FONT>                    }<a name="line.1959"></a>
<FONT color="green">1960</FONT>                }<a name="line.1960"></a>
<FONT color="green">1961</FONT>    <a name="line.1961"></a>
<FONT color="green">1962</FONT>                // Update CRVMIN, GNEW and D. Set SDEC to the decrease that occurs in Q.<a name="line.1962"></a>
<FONT color="green">1963</FONT>    <a name="line.1963"></a>
<FONT color="green">1964</FONT>                sdec = ZERO;<a name="line.1964"></a>
<FONT color="green">1965</FONT>                if (stplen &gt; ZERO) {<a name="line.1965"></a>
<FONT color="green">1966</FONT>                    ++iterc;<a name="line.1966"></a>
<FONT color="green">1967</FONT>                    temp = shs / stepsq;<a name="line.1967"></a>
<FONT color="green">1968</FONT>                    if (iact == -1 &amp;&amp; temp &gt; ZERO) {<a name="line.1968"></a>
<FONT color="green">1969</FONT>                        crvmin = Math.min(crvmin,temp);<a name="line.1969"></a>
<FONT color="green">1970</FONT>                        if (crvmin == MINUS_ONE) {<a name="line.1970"></a>
<FONT color="green">1971</FONT>                            crvmin = temp;<a name="line.1971"></a>
<FONT color="green">1972</FONT>                        }<a name="line.1972"></a>
<FONT color="green">1973</FONT>                    }<a name="line.1973"></a>
<FONT color="green">1974</FONT>                    ggsav = gredsq;<a name="line.1974"></a>
<FONT color="green">1975</FONT>                    gredsq = ZERO;<a name="line.1975"></a>
<FONT color="green">1976</FONT>                    for (int i = 0; i &lt; n; i++) {<a name="line.1976"></a>
<FONT color="green">1977</FONT>                        gnew.setEntry(i, gnew.getEntry(i) + stplen * hs.getEntry(i));<a name="line.1977"></a>
<FONT color="green">1978</FONT>                        if (xbdi.getEntry(i) == ZERO) {<a name="line.1978"></a>
<FONT color="green">1979</FONT>                            // Computing 2nd power<a name="line.1979"></a>
<FONT color="green">1980</FONT>                            final double d1 = gnew.getEntry(i);<a name="line.1980"></a>
<FONT color="green">1981</FONT>                            gredsq += d1 * d1;<a name="line.1981"></a>
<FONT color="green">1982</FONT>                        }<a name="line.1982"></a>
<FONT color="green">1983</FONT>                        trialStepPoint.setEntry(i, trialStepPoint.getEntry(i) + stplen * s.getEntry(i));<a name="line.1983"></a>
<FONT color="green">1984</FONT>                    }<a name="line.1984"></a>
<FONT color="green">1985</FONT>                    // Computing MAX<a name="line.1985"></a>
<FONT color="green">1986</FONT>                    final double d1 = stplen * (ggsav - HALF * stplen * shs);<a name="line.1986"></a>
<FONT color="green">1987</FONT>                    sdec = Math.max(d1, ZERO);<a name="line.1987"></a>
<FONT color="green">1988</FONT>                    qred += sdec;<a name="line.1988"></a>
<FONT color="green">1989</FONT>                }<a name="line.1989"></a>
<FONT color="green">1990</FONT>    <a name="line.1990"></a>
<FONT color="green">1991</FONT>                // Restart the conjugate gradient method if it has hit a new bound.<a name="line.1991"></a>
<FONT color="green">1992</FONT>    <a name="line.1992"></a>
<FONT color="green">1993</FONT>                if (iact &gt;= 0) {<a name="line.1993"></a>
<FONT color="green">1994</FONT>                    ++nact;<a name="line.1994"></a>
<FONT color="green">1995</FONT>                    xbdi.setEntry(iact, ONE);<a name="line.1995"></a>
<FONT color="green">1996</FONT>                    if (s.getEntry(iact) &lt; ZERO) {<a name="line.1996"></a>
<FONT color="green">1997</FONT>                        xbdi.setEntry(iact, MINUS_ONE);<a name="line.1997"></a>
<FONT color="green">1998</FONT>                    }<a name="line.1998"></a>
<FONT color="green">1999</FONT>                    // Computing 2nd power<a name="line.1999"></a>
<FONT color="green">2000</FONT>                    final double d1 = trialStepPoint.getEntry(iact);<a name="line.2000"></a>
<FONT color="green">2001</FONT>                    delsq -= d1 * d1;<a name="line.2001"></a>
<FONT color="green">2002</FONT>                    if (delsq &lt;= ZERO) {<a name="line.2002"></a>
<FONT color="green">2003</FONT>                        state = 190; break;<a name="line.2003"></a>
<FONT color="green">2004</FONT>                    }<a name="line.2004"></a>
<FONT color="green">2005</FONT>                    state = 20; break;<a name="line.2005"></a>
<FONT color="green">2006</FONT>                }<a name="line.2006"></a>
<FONT color="green">2007</FONT>    <a name="line.2007"></a>
<FONT color="green">2008</FONT>                // If STPLEN is less than BLEN, then either apply another conjugate<a name="line.2008"></a>
<FONT color="green">2009</FONT>                // gradient iteration or RETURN.<a name="line.2009"></a>
<FONT color="green">2010</FONT>    <a name="line.2010"></a>
<FONT color="green">2011</FONT>                if (stplen &lt; blen) {<a name="line.2011"></a>
<FONT color="green">2012</FONT>                    if (iterc == itermax) {<a name="line.2012"></a>
<FONT color="green">2013</FONT>                        state = 190; break;<a name="line.2013"></a>
<FONT color="green">2014</FONT>                    }<a name="line.2014"></a>
<FONT color="green">2015</FONT>                    if (sdec &lt;= qred * .01) {<a name="line.2015"></a>
<FONT color="green">2016</FONT>                        state = 190; break;<a name="line.2016"></a>
<FONT color="green">2017</FONT>                    }<a name="line.2017"></a>
<FONT color="green">2018</FONT>                    beta = gredsq / ggsav;<a name="line.2018"></a>
<FONT color="green">2019</FONT>                    state = 30; break;<a name="line.2019"></a>
<FONT color="green">2020</FONT>                }<a name="line.2020"></a>
<FONT color="green">2021</FONT>            }<a name="line.2021"></a>
<FONT color="green">2022</FONT>            case 90: {<a name="line.2022"></a>
<FONT color="green">2023</FONT>                printState(90); // XXX<a name="line.2023"></a>
<FONT color="green">2024</FONT>                crvmin = ZERO;<a name="line.2024"></a>
<FONT color="green">2025</FONT>    <a name="line.2025"></a>
<FONT color="green">2026</FONT>                // Prepare for the alternative iteration by calculating some scalars<a name="line.2026"></a>
<FONT color="green">2027</FONT>                // and by multiplying the reduced D by the second derivative matrix of<a name="line.2027"></a>
<FONT color="green">2028</FONT>                // Q, where S holds the reduced D in the call of GGMULT.<a name="line.2028"></a>
<FONT color="green">2029</FONT>    <a name="line.2029"></a>
<FONT color="green">2030</FONT>            }<a name="line.2030"></a>
<FONT color="green">2031</FONT>            case 100: {<a name="line.2031"></a>
<FONT color="green">2032</FONT>                printState(100); // XXX<a name="line.2032"></a>
<FONT color="green">2033</FONT>                if (nact &gt;= n - 1) {<a name="line.2033"></a>
<FONT color="green">2034</FONT>                    state = 190; break;<a name="line.2034"></a>
<FONT color="green">2035</FONT>                }<a name="line.2035"></a>
<FONT color="green">2036</FONT>                dredsq = ZERO;<a name="line.2036"></a>
<FONT color="green">2037</FONT>                dredg = ZERO;<a name="line.2037"></a>
<FONT color="green">2038</FONT>                gredsq = ZERO;<a name="line.2038"></a>
<FONT color="green">2039</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.2039"></a>
<FONT color="green">2040</FONT>                    if (xbdi.getEntry(i) == ZERO) {<a name="line.2040"></a>
<FONT color="green">2041</FONT>                        // Computing 2nd power<a name="line.2041"></a>
<FONT color="green">2042</FONT>                        double d1 = trialStepPoint.getEntry(i);<a name="line.2042"></a>
<FONT color="green">2043</FONT>                        dredsq += d1 * d1;<a name="line.2043"></a>
<FONT color="green">2044</FONT>                        dredg += trialStepPoint.getEntry(i) * gnew.getEntry(i);<a name="line.2044"></a>
<FONT color="green">2045</FONT>                        // Computing 2nd power<a name="line.2045"></a>
<FONT color="green">2046</FONT>                        d1 = gnew.getEntry(i);<a name="line.2046"></a>
<FONT color="green">2047</FONT>                        gredsq += d1 * d1;<a name="line.2047"></a>
<FONT color="green">2048</FONT>                        s.setEntry(i, trialStepPoint.getEntry(i));<a name="line.2048"></a>
<FONT color="green">2049</FONT>                    } else {<a name="line.2049"></a>
<FONT color="green">2050</FONT>                        s.setEntry(i, ZERO);<a name="line.2050"></a>
<FONT color="green">2051</FONT>                    }<a name="line.2051"></a>
<FONT color="green">2052</FONT>                }<a name="line.2052"></a>
<FONT color="green">2053</FONT>                itcsav = iterc;<a name="line.2053"></a>
<FONT color="green">2054</FONT>                state = 210; break;<a name="line.2054"></a>
<FONT color="green">2055</FONT>                // Let the search direction S be a linear combination of the reduced D<a name="line.2055"></a>
<FONT color="green">2056</FONT>                // and the reduced G that is orthogonal to the reduced D.<a name="line.2056"></a>
<FONT color="green">2057</FONT>            }<a name="line.2057"></a>
<FONT color="green">2058</FONT>            case 120: {<a name="line.2058"></a>
<FONT color="green">2059</FONT>                printState(120); // XXX<a name="line.2059"></a>
<FONT color="green">2060</FONT>                ++iterc;<a name="line.2060"></a>
<FONT color="green">2061</FONT>                temp = gredsq * dredsq - dredg * dredg;<a name="line.2061"></a>
<FONT color="green">2062</FONT>                if (temp &lt;= qred * 1e-4 * qred) {<a name="line.2062"></a>
<FONT color="green">2063</FONT>                    state = 190; break;<a name="line.2063"></a>
<FONT color="green">2064</FONT>                }<a name="line.2064"></a>
<FONT color="green">2065</FONT>                temp = Math.sqrt(temp);<a name="line.2065"></a>
<FONT color="green">2066</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.2066"></a>
<FONT color="green">2067</FONT>                    if (xbdi.getEntry(i) == ZERO) {<a name="line.2067"></a>
<FONT color="green">2068</FONT>                        s.setEntry(i, (dredg * trialStepPoint.getEntry(i) - dredsq * gnew.getEntry(i)) / temp);<a name="line.2068"></a>
<FONT color="green">2069</FONT>                    } else {<a name="line.2069"></a>
<FONT color="green">2070</FONT>                        s.setEntry(i, ZERO);<a name="line.2070"></a>
<FONT color="green">2071</FONT>                    }<a name="line.2071"></a>
<FONT color="green">2072</FONT>                }<a name="line.2072"></a>
<FONT color="green">2073</FONT>                sredg = -temp;<a name="line.2073"></a>
<FONT color="green">2074</FONT>    <a name="line.2074"></a>
<FONT color="green">2075</FONT>                // By considering the simple bounds on the variables, calculate an upper<a name="line.2075"></a>
<FONT color="green">2076</FONT>                // bound on the tangent of half the angle of the alternative iteration,<a name="line.2076"></a>
<FONT color="green">2077</FONT>                // namely ANGBD, except that, if already a free variable has reached a<a name="line.2077"></a>
<FONT color="green">2078</FONT>                // bound, there is a branch back to label 100 after fixing that variable.<a name="line.2078"></a>
<FONT color="green">2079</FONT>    <a name="line.2079"></a>
<FONT color="green">2080</FONT>                angbd = ONE;<a name="line.2080"></a>
<FONT color="green">2081</FONT>                iact = -1;<a name="line.2081"></a>
<FONT color="green">2082</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.2082"></a>
<FONT color="green">2083</FONT>                    if (xbdi.getEntry(i) == ZERO) {<a name="line.2083"></a>
<FONT color="green">2084</FONT>                        tempa = trustRegionCenterOffset.getEntry(i) + trialStepPoint.getEntry(i) - lowerDifference.getEntry(i);<a name="line.2084"></a>
<FONT color="green">2085</FONT>                        tempb = upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i) - trialStepPoint.getEntry(i);<a name="line.2085"></a>
<FONT color="green">2086</FONT>                        if (tempa &lt;= ZERO) {<a name="line.2086"></a>
<FONT color="green">2087</FONT>                            ++nact;<a name="line.2087"></a>
<FONT color="green">2088</FONT>                            xbdi.setEntry(i, MINUS_ONE);<a name="line.2088"></a>
<FONT color="green">2089</FONT>                            state = 100; break;<a name="line.2089"></a>
<FONT color="green">2090</FONT>                        } else if (tempb &lt;= ZERO) {<a name="line.2090"></a>
<FONT color="green">2091</FONT>                            ++nact;<a name="line.2091"></a>
<FONT color="green">2092</FONT>                            xbdi.setEntry(i, ONE);<a name="line.2092"></a>
<FONT color="green">2093</FONT>                            state = 100; break;<a name="line.2093"></a>
<FONT color="green">2094</FONT>                        }<a name="line.2094"></a>
<FONT color="green">2095</FONT>                        // Computing 2nd power<a name="line.2095"></a>
<FONT color="green">2096</FONT>                        double d1 = trialStepPoint.getEntry(i);<a name="line.2096"></a>
<FONT color="green">2097</FONT>                        // Computing 2nd power<a name="line.2097"></a>
<FONT color="green">2098</FONT>                        double d2 = s.getEntry(i);<a name="line.2098"></a>
<FONT color="green">2099</FONT>                        ssq = d1 * d1 + d2 * d2;<a name="line.2099"></a>
<FONT color="green">2100</FONT>                        // Computing 2nd power<a name="line.2100"></a>
<FONT color="green">2101</FONT>                        d1 = trustRegionCenterOffset.getEntry(i) - lowerDifference.getEntry(i);<a name="line.2101"></a>
<FONT color="green">2102</FONT>                        temp = ssq - d1 * d1;<a name="line.2102"></a>
<FONT color="green">2103</FONT>                        if (temp &gt; ZERO) {<a name="line.2103"></a>
<FONT color="green">2104</FONT>                            temp = Math.sqrt(temp) - s.getEntry(i);<a name="line.2104"></a>
<FONT color="green">2105</FONT>                            if (angbd * temp &gt; tempa) {<a name="line.2105"></a>
<FONT color="green">2106</FONT>                                angbd = tempa / temp;<a name="line.2106"></a>
<FONT color="green">2107</FONT>                                iact = i;<a name="line.2107"></a>
<FONT color="green">2108</FONT>                                xsav = MINUS_ONE;<a name="line.2108"></a>
<FONT color="green">2109</FONT>                            }<a name="line.2109"></a>
<FONT color="green">2110</FONT>                        }<a name="line.2110"></a>
<FONT color="green">2111</FONT>                        // Computing 2nd power<a name="line.2111"></a>
<FONT color="green">2112</FONT>                        d1 = upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i);<a name="line.2112"></a>
<FONT color="green">2113</FONT>                        temp = ssq - d1 * d1;<a name="line.2113"></a>
<FONT color="green">2114</FONT>                        if (temp &gt; ZERO) {<a name="line.2114"></a>
<FONT color="green">2115</FONT>                            temp = Math.sqrt(temp) + s.getEntry(i);<a name="line.2115"></a>
<FONT color="green">2116</FONT>                            if (angbd * temp &gt; tempb) {<a name="line.2116"></a>
<FONT color="green">2117</FONT>                                angbd = tempb / temp;<a name="line.2117"></a>
<FONT color="green">2118</FONT>                                iact = i;<a name="line.2118"></a>
<FONT color="green">2119</FONT>                                xsav = ONE;<a name="line.2119"></a>
<FONT color="green">2120</FONT>                            }<a name="line.2120"></a>
<FONT color="green">2121</FONT>                        }<a name="line.2121"></a>
<FONT color="green">2122</FONT>                    }<a name="line.2122"></a>
<FONT color="green">2123</FONT>                }<a name="line.2123"></a>
<FONT color="green">2124</FONT>    <a name="line.2124"></a>
<FONT color="green">2125</FONT>                // Calculate HHD and some curvatures for the alternative iteration.<a name="line.2125"></a>
<FONT color="green">2126</FONT>    <a name="line.2126"></a>
<FONT color="green">2127</FONT>                state = 210; break;<a name="line.2127"></a>
<FONT color="green">2128</FONT>            }<a name="line.2128"></a>
<FONT color="green">2129</FONT>            case 150: {<a name="line.2129"></a>
<FONT color="green">2130</FONT>                printState(150); // XXX<a name="line.2130"></a>
<FONT color="green">2131</FONT>                shs = ZERO;<a name="line.2131"></a>
<FONT color="green">2132</FONT>                dhs = ZERO;<a name="line.2132"></a>
<FONT color="green">2133</FONT>                dhd = ZERO;<a name="line.2133"></a>
<FONT color="green">2134</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.2134"></a>
<FONT color="green">2135</FONT>                    if (xbdi.getEntry(i) == ZERO) {<a name="line.2135"></a>
<FONT color="green">2136</FONT>                        shs += s.getEntry(i) * hs.getEntry(i);<a name="line.2136"></a>
<FONT color="green">2137</FONT>                        dhs += trialStepPoint.getEntry(i) * hs.getEntry(i);<a name="line.2137"></a>
<FONT color="green">2138</FONT>                        dhd += trialStepPoint.getEntry(i) * hred.getEntry(i);<a name="line.2138"></a>
<FONT color="green">2139</FONT>                    }<a name="line.2139"></a>
<FONT color="green">2140</FONT>                }<a name="line.2140"></a>
<FONT color="green">2141</FONT>    <a name="line.2141"></a>
<FONT color="green">2142</FONT>                // Seek the greatest reduction in Q for a range of equally spaced values<a name="line.2142"></a>
<FONT color="green">2143</FONT>                // of ANGT in [0,ANGBD], where ANGT is the tangent of half the angle of<a name="line.2143"></a>
<FONT color="green">2144</FONT>                // the alternative iteration.<a name="line.2144"></a>
<FONT color="green">2145</FONT>    <a name="line.2145"></a>
<FONT color="green">2146</FONT>                redmax = ZERO;<a name="line.2146"></a>
<FONT color="green">2147</FONT>                isav = -1;<a name="line.2147"></a>
<FONT color="green">2148</FONT>                redsav = ZERO;<a name="line.2148"></a>
<FONT color="green">2149</FONT>                iu = (int) (angbd * 17. + 3.1);<a name="line.2149"></a>
<FONT color="green">2150</FONT>                for (int i = 0; i &lt; iu; i++) {<a name="line.2150"></a>
<FONT color="green">2151</FONT>                    angt = angbd * i / iu;<a name="line.2151"></a>
<FONT color="green">2152</FONT>                    sth = (angt + angt) / (ONE + angt * angt);<a name="line.2152"></a>
<FONT color="green">2153</FONT>                    temp = shs + angt * (angt * dhd - dhs - dhs);<a name="line.2153"></a>
<FONT color="green">2154</FONT>                    rednew = sth * (angt * dredg - sredg - HALF * sth * temp);<a name="line.2154"></a>
<FONT color="green">2155</FONT>                    if (rednew &gt; redmax) {<a name="line.2155"></a>
<FONT color="green">2156</FONT>                        redmax = rednew;<a name="line.2156"></a>
<FONT color="green">2157</FONT>                        isav = i;<a name="line.2157"></a>
<FONT color="green">2158</FONT>                        rdprev = redsav;<a name="line.2158"></a>
<FONT color="green">2159</FONT>                    } else if (i == isav + 1) {<a name="line.2159"></a>
<FONT color="green">2160</FONT>                        rdnext = rednew;<a name="line.2160"></a>
<FONT color="green">2161</FONT>                    }<a name="line.2161"></a>
<FONT color="green">2162</FONT>                    redsav = rednew;<a name="line.2162"></a>
<FONT color="green">2163</FONT>                }<a name="line.2163"></a>
<FONT color="green">2164</FONT>    <a name="line.2164"></a>
<FONT color="green">2165</FONT>                // Return if the reduction is zero. Otherwise, set the sine and cosine<a name="line.2165"></a>
<FONT color="green">2166</FONT>                // of the angle of the alternative iteration, and calculate SDEC.<a name="line.2166"></a>
<FONT color="green">2167</FONT>    <a name="line.2167"></a>
<FONT color="green">2168</FONT>                if (isav &lt; 0) {<a name="line.2168"></a>
<FONT color="green">2169</FONT>                    state = 190; break;<a name="line.2169"></a>
<FONT color="green">2170</FONT>                }<a name="line.2170"></a>
<FONT color="green">2171</FONT>                if (isav &lt; iu) {<a name="line.2171"></a>
<FONT color="green">2172</FONT>                    temp = (rdnext - rdprev) / (redmax + redmax - rdprev - rdnext);<a name="line.2172"></a>
<FONT color="green">2173</FONT>                    angt = angbd * (isav + HALF * temp) / iu;<a name="line.2173"></a>
<FONT color="green">2174</FONT>                }<a name="line.2174"></a>
<FONT color="green">2175</FONT>                cth = (ONE - angt * angt) / (ONE + angt * angt);<a name="line.2175"></a>
<FONT color="green">2176</FONT>                sth = (angt + angt) / (ONE + angt * angt);<a name="line.2176"></a>
<FONT color="green">2177</FONT>                temp = shs + angt * (angt * dhd - dhs - dhs);<a name="line.2177"></a>
<FONT color="green">2178</FONT>                sdec = sth * (angt * dredg - sredg - HALF * sth * temp);<a name="line.2178"></a>
<FONT color="green">2179</FONT>                if (sdec &lt;= ZERO) {<a name="line.2179"></a>
<FONT color="green">2180</FONT>                    state = 190; break;<a name="line.2180"></a>
<FONT color="green">2181</FONT>                }<a name="line.2181"></a>
<FONT color="green">2182</FONT>    <a name="line.2182"></a>
<FONT color="green">2183</FONT>                // Update GNEW, D and HRED. If the angle of the alternative iteration<a name="line.2183"></a>
<FONT color="green">2184</FONT>                // is restricted by a bound on a free variable, that variable is fixed<a name="line.2184"></a>
<FONT color="green">2185</FONT>                // at the bound.<a name="line.2185"></a>
<FONT color="green">2186</FONT>    <a name="line.2186"></a>
<FONT color="green">2187</FONT>                dredg = ZERO;<a name="line.2187"></a>
<FONT color="green">2188</FONT>                gredsq = ZERO;<a name="line.2188"></a>
<FONT color="green">2189</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.2189"></a>
<FONT color="green">2190</FONT>                    gnew.setEntry(i, gnew.getEntry(i) + (cth - ONE) * hred.getEntry(i) + sth * hs.getEntry(i));<a name="line.2190"></a>
<FONT color="green">2191</FONT>                    if (xbdi.getEntry(i) == ZERO) {<a name="line.2191"></a>
<FONT color="green">2192</FONT>                        trialStepPoint.setEntry(i, cth * trialStepPoint.getEntry(i) + sth * s.getEntry(i));<a name="line.2192"></a>
<FONT color="green">2193</FONT>                        dredg += trialStepPoint.getEntry(i) * gnew.getEntry(i);<a name="line.2193"></a>
<FONT color="green">2194</FONT>                        // Computing 2nd power<a name="line.2194"></a>
<FONT color="green">2195</FONT>                        final double d1 = gnew.getEntry(i);<a name="line.2195"></a>
<FONT color="green">2196</FONT>                        gredsq += d1 * d1;<a name="line.2196"></a>
<FONT color="green">2197</FONT>                    }<a name="line.2197"></a>
<FONT color="green">2198</FONT>                    hred.setEntry(i, cth * hred.getEntry(i) + sth * hs.getEntry(i));<a name="line.2198"></a>
<FONT color="green">2199</FONT>                }<a name="line.2199"></a>
<FONT color="green">2200</FONT>                qred += sdec;<a name="line.2200"></a>
<FONT color="green">2201</FONT>                if (iact &gt;= 0 &amp;&amp; isav == iu) {<a name="line.2201"></a>
<FONT color="green">2202</FONT>                    ++nact;<a name="line.2202"></a>
<FONT color="green">2203</FONT>                    xbdi.setEntry(iact, xsav);<a name="line.2203"></a>
<FONT color="green">2204</FONT>                    state = 100; break;<a name="line.2204"></a>
<FONT color="green">2205</FONT>                }<a name="line.2205"></a>
<FONT color="green">2206</FONT>    <a name="line.2206"></a>
<FONT color="green">2207</FONT>                // If SDEC is sufficiently small, then RETURN after setting XNEW to<a name="line.2207"></a>
<FONT color="green">2208</FONT>                // XOPT+D, giving careful attention to the bounds.<a name="line.2208"></a>
<FONT color="green">2209</FONT>    <a name="line.2209"></a>
<FONT color="green">2210</FONT>                if (sdec &gt; qred * .01) {<a name="line.2210"></a>
<FONT color="green">2211</FONT>                    state = 120; break;<a name="line.2211"></a>
<FONT color="green">2212</FONT>                }<a name="line.2212"></a>
<FONT color="green">2213</FONT>            }<a name="line.2213"></a>
<FONT color="green">2214</FONT>            case 190: {<a name="line.2214"></a>
<FONT color="green">2215</FONT>                printState(190); // XXX<a name="line.2215"></a>
<FONT color="green">2216</FONT>                dsq = ZERO;<a name="line.2216"></a>
<FONT color="green">2217</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.2217"></a>
<FONT color="green">2218</FONT>                    // Computing MAX<a name="line.2218"></a>
<FONT color="green">2219</FONT>                    // Computing MIN<a name="line.2219"></a>
<FONT color="green">2220</FONT>                    final double min = Math.min(trustRegionCenterOffset.getEntry(i) + trialStepPoint.getEntry(i),<a name="line.2220"></a>
<FONT color="green">2221</FONT>                                                upperDifference.getEntry(i));<a name="line.2221"></a>
<FONT color="green">2222</FONT>                    newPoint.setEntry(i, Math.max(min, lowerDifference.getEntry(i)));<a name="line.2222"></a>
<FONT color="green">2223</FONT>                    if (xbdi.getEntry(i) == MINUS_ONE) {<a name="line.2223"></a>
<FONT color="green">2224</FONT>                        newPoint.setEntry(i, lowerDifference.getEntry(i));<a name="line.2224"></a>
<FONT color="green">2225</FONT>                    }<a name="line.2225"></a>
<FONT color="green">2226</FONT>                    if (xbdi.getEntry(i) == ONE) {<a name="line.2226"></a>
<FONT color="green">2227</FONT>                        newPoint.setEntry(i, upperDifference.getEntry(i));<a name="line.2227"></a>
<FONT color="green">2228</FONT>                    }<a name="line.2228"></a>
<FONT color="green">2229</FONT>                    trialStepPoint.setEntry(i, newPoint.getEntry(i) - trustRegionCenterOffset.getEntry(i));<a name="line.2229"></a>
<FONT color="green">2230</FONT>                    // Computing 2nd power<a name="line.2230"></a>
<FONT color="green">2231</FONT>                    final double d1 = trialStepPoint.getEntry(i);<a name="line.2231"></a>
<FONT color="green">2232</FONT>                    dsq += d1 * d1;<a name="line.2232"></a>
<FONT color="green">2233</FONT>                }<a name="line.2233"></a>
<FONT color="green">2234</FONT>                return new double[] { dsq, crvmin };<a name="line.2234"></a>
<FONT color="green">2235</FONT>                // The following instructions multiply the current S-vector by the second<a name="line.2235"></a>
<FONT color="green">2236</FONT>                // derivative matrix of the quadratic model, putting the product in HS.<a name="line.2236"></a>
<FONT color="green">2237</FONT>                // They are reached from three different parts of the software above and<a name="line.2237"></a>
<FONT color="green">2238</FONT>                // they can be regarded as an external subroutine.<a name="line.2238"></a>
<FONT color="green">2239</FONT>            }<a name="line.2239"></a>
<FONT color="green">2240</FONT>            case 210: {<a name="line.2240"></a>
<FONT color="green">2241</FONT>                printState(210); // XXX<a name="line.2241"></a>
<FONT color="green">2242</FONT>                int ih = 0;<a name="line.2242"></a>
<FONT color="green">2243</FONT>                for (int j = 0; j &lt; n; j++) {<a name="line.2243"></a>
<FONT color="green">2244</FONT>                    hs.setEntry(j, ZERO);<a name="line.2244"></a>
<FONT color="green">2245</FONT>                    for (int i = 0; i &lt;= j; i++) {<a name="line.2245"></a>
<FONT color="green">2246</FONT>                        if (i &lt; j) {<a name="line.2246"></a>
<FONT color="green">2247</FONT>                            hs.setEntry(j, hs.getEntry(j) + modelSecondDerivativesValues.getEntry(ih) * s.getEntry(i));<a name="line.2247"></a>
<FONT color="green">2248</FONT>                        }<a name="line.2248"></a>
<FONT color="green">2249</FONT>                        hs.setEntry(i, hs.getEntry(i) + modelSecondDerivativesValues.getEntry(ih) * s.getEntry(j));<a name="line.2249"></a>
<FONT color="green">2250</FONT>                        ih++;<a name="line.2250"></a>
<FONT color="green">2251</FONT>                    }<a name="line.2251"></a>
<FONT color="green">2252</FONT>                }<a name="line.2252"></a>
<FONT color="green">2253</FONT>                final RealVector tmp = interpolationPoints.operate(s).ebeMultiply(modelSecondDerivativesParameters);<a name="line.2253"></a>
<FONT color="green">2254</FONT>                for (int k = 0; k &lt; npt; k++) {<a name="line.2254"></a>
<FONT color="green">2255</FONT>                    if (modelSecondDerivativesParameters.getEntry(k) != ZERO) {<a name="line.2255"></a>
<FONT color="green">2256</FONT>                        for (int i = 0; i &lt; n; i++) {<a name="line.2256"></a>
<FONT color="green">2257</FONT>                            hs.setEntry(i, hs.getEntry(i) + tmp.getEntry(k) * interpolationPoints.getEntry(k, i));<a name="line.2257"></a>
<FONT color="green">2258</FONT>                        }<a name="line.2258"></a>
<FONT color="green">2259</FONT>                    }<a name="line.2259"></a>
<FONT color="green">2260</FONT>                }<a name="line.2260"></a>
<FONT color="green">2261</FONT>                if (crvmin != ZERO) {<a name="line.2261"></a>
<FONT color="green">2262</FONT>                    state = 50; break;<a name="line.2262"></a>
<FONT color="green">2263</FONT>                }<a name="line.2263"></a>
<FONT color="green">2264</FONT>                if (iterc &gt; itcsav) {<a name="line.2264"></a>
<FONT color="green">2265</FONT>                    state = 150; break;<a name="line.2265"></a>
<FONT color="green">2266</FONT>                }<a name="line.2266"></a>
<FONT color="green">2267</FONT>                for (int i = 0; i &lt; n; i++) {<a name="line.2267"></a>
<FONT color="green">2268</FONT>                    hred.setEntry(i, hs.getEntry(i));<a name="line.2268"></a>
<FONT color="green">2269</FONT>                }<a name="line.2269"></a>
<FONT color="green">2270</FONT>                state = 120; break;<a name="line.2270"></a>
<FONT color="green">2271</FONT>            }<a name="line.2271"></a>
<FONT color="green">2272</FONT>            default: {<a name="line.2272"></a>
<FONT color="green">2273</FONT>                throw new MathIllegalStateException(LocalizedFormats.SIMPLE_MESSAGE, "trsbox");<a name="line.2273"></a>
<FONT color="green">2274</FONT>            }}<a name="line.2274"></a>
<FONT color="green">2275</FONT>            }<a name="line.2275"></a>
<FONT color="green">2276</FONT>        } // trsbox<a name="line.2276"></a>
<FONT color="green">2277</FONT>    <a name="line.2277"></a>
<FONT color="green">2278</FONT>        // ----------------------------------------------------------------------------------------<a name="line.2278"></a>
<FONT color="green">2279</FONT>    <a name="line.2279"></a>
<FONT color="green">2280</FONT>        /**<a name="line.2280"></a>
<FONT color="green">2281</FONT>         *     The arrays BMAT and ZMAT are updated, as required by the new position<a name="line.2281"></a>
<FONT color="green">2282</FONT>         *     of the interpolation point that has the index KNEW. The vector VLAG has<a name="line.2282"></a>
<FONT color="green">2283</FONT>         *     N+NPT components, set on entry to the first NPT and last N components<a name="line.2283"></a>
<FONT color="green">2284</FONT>         *     of the product Hw in equation (4.11) of the Powell (2006) paper on<a name="line.2284"></a>
<FONT color="green">2285</FONT>         *     NEWUOA. Further, BETA is set on entry to the value of the parameter<a name="line.2285"></a>
<FONT color="green">2286</FONT>         *     with that name, and DENOM is set to the denominator of the updating<a name="line.2286"></a>
<FONT color="green">2287</FONT>         *     formula. Elements of ZMAT may be treated as zero if their moduli are<a name="line.2287"></a>
<FONT color="green">2288</FONT>         *     at most ZTEST. The first NDIM elements of W are used for working space.<a name="line.2288"></a>
<FONT color="green">2289</FONT>         * @param beta<a name="line.2289"></a>
<FONT color="green">2290</FONT>         * @param denom<a name="line.2290"></a>
<FONT color="green">2291</FONT>         * @param knew<a name="line.2291"></a>
<FONT color="green">2292</FONT>         */<a name="line.2292"></a>
<FONT color="green">2293</FONT>        private void update(<a name="line.2293"></a>
<FONT color="green">2294</FONT>                double beta,<a name="line.2294"></a>
<FONT color="green">2295</FONT>                double denom,<a name="line.2295"></a>
<FONT color="green">2296</FONT>                int knew<a name="line.2296"></a>
<FONT color="green">2297</FONT>        ) {<a name="line.2297"></a>
<FONT color="green">2298</FONT>            printMethod(); // XXX<a name="line.2298"></a>
<FONT color="green">2299</FONT>    <a name="line.2299"></a>
<FONT color="green">2300</FONT>            final int n = currentBest.getDimension();<a name="line.2300"></a>
<FONT color="green">2301</FONT>            final int npt = numberOfInterpolationPoints;<a name="line.2301"></a>
<FONT color="green">2302</FONT>            final int nptm = npt - n - 1;<a name="line.2302"></a>
<FONT color="green">2303</FONT>    <a name="line.2303"></a>
<FONT color="green">2304</FONT>            // XXX Should probably be split into two arrays.<a name="line.2304"></a>
<FONT color="green">2305</FONT>            final ArrayRealVector work = new ArrayRealVector(npt + n);<a name="line.2305"></a>
<FONT color="green">2306</FONT>    <a name="line.2306"></a>
<FONT color="green">2307</FONT>            double ztest = ZERO;<a name="line.2307"></a>
<FONT color="green">2308</FONT>            for (int k = 0; k &lt; npt; k++) {<a name="line.2308"></a>
<FONT color="green">2309</FONT>                for (int j = 0; j &lt; nptm; j++) {<a name="line.2309"></a>
<FONT color="green">2310</FONT>                    // Computing MAX<a name="line.2310"></a>
<FONT color="green">2311</FONT>                    ztest = Math.max(ztest, Math.abs(zMatrix.getEntry(k, j)));<a name="line.2311"></a>
<FONT color="green">2312</FONT>                }<a name="line.2312"></a>
<FONT color="green">2313</FONT>            }<a name="line.2313"></a>
<FONT color="green">2314</FONT>            ztest *= 1e-20;<a name="line.2314"></a>
<FONT color="green">2315</FONT>    <a name="line.2315"></a>
<FONT color="green">2316</FONT>            // Apply the rotations that put zeros in the KNEW-th row of ZMAT.<a name="line.2316"></a>
<FONT color="green">2317</FONT>    <a name="line.2317"></a>
<FONT color="green">2318</FONT>            for (int j = 1; j &lt; nptm; j++) {<a name="line.2318"></a>
<FONT color="green">2319</FONT>                final double d1 = zMatrix.getEntry(knew, j);<a name="line.2319"></a>
<FONT color="green">2320</FONT>                if (Math.abs(d1) &gt; ztest) {<a name="line.2320"></a>
<FONT color="green">2321</FONT>                    // Computing 2nd power<a name="line.2321"></a>
<FONT color="green">2322</FONT>                    final double d2 = zMatrix.getEntry(knew, 0);<a name="line.2322"></a>
<FONT color="green">2323</FONT>                    // Computing 2nd power<a name="line.2323"></a>
<FONT color="green">2324</FONT>                    final double d3 = zMatrix.getEntry(knew, j);<a name="line.2324"></a>
<FONT color="green">2325</FONT>                    final double d4 = Math.sqrt(d2 * d2 + d3 * d3);<a name="line.2325"></a>
<FONT color="green">2326</FONT>                    final double d5 = zMatrix.getEntry(knew, 0) / d4;<a name="line.2326"></a>
<FONT color="green">2327</FONT>                    final double d6 = zMatrix.getEntry(knew, j) / d4;<a name="line.2327"></a>
<FONT color="green">2328</FONT>                    for (int i = 0; i &lt; npt; i++) {<a name="line.2328"></a>
<FONT color="green">2329</FONT>                        final double d7 = d5 * zMatrix.getEntry(i, 0) + d6 * zMatrix.getEntry(i, j);<a name="line.2329"></a>
<FONT color="green">2330</FONT>                        zMatrix.setEntry(i, j, d5 * zMatrix.getEntry(i, j) - d6 * zMatrix.getEntry(i, 0));<a name="line.2330"></a>
<FONT color="green">2331</FONT>                        zMatrix.setEntry(i, 0, d7);<a name="line.2331"></a>
<FONT color="green">2332</FONT>                    }<a name="line.2332"></a>
<FONT color="green">2333</FONT>                }<a name="line.2333"></a>
<FONT color="green">2334</FONT>                zMatrix.setEntry(knew, j, ZERO);<a name="line.2334"></a>
<FONT color="green">2335</FONT>            }<a name="line.2335"></a>
<FONT color="green">2336</FONT>    <a name="line.2336"></a>
<FONT color="green">2337</FONT>            // Put the first NPT components of the KNEW-th column of HLAG into W,<a name="line.2337"></a>
<FONT color="green">2338</FONT>            // and calculate the parameters of the updating formula.<a name="line.2338"></a>
<FONT color="green">2339</FONT>    <a name="line.2339"></a>
<FONT color="green">2340</FONT>            for (int i = 0; i &lt; npt; i++) {<a name="line.2340"></a>
<FONT color="green">2341</FONT>                work.setEntry(i, zMatrix.getEntry(knew, 0) * zMatrix.getEntry(i, 0));<a name="line.2341"></a>
<FONT color="green">2342</FONT>            }<a name="line.2342"></a>
<FONT color="green">2343</FONT>            final double alpha = work.getEntry(knew);<a name="line.2343"></a>
<FONT color="green">2344</FONT>            final double tau = lagrangeValuesAtNewPoint.getEntry(knew);<a name="line.2344"></a>
<FONT color="green">2345</FONT>            lagrangeValuesAtNewPoint.setEntry(knew, lagrangeValuesAtNewPoint.getEntry(knew) - ONE);<a name="line.2345"></a>
<FONT color="green">2346</FONT>    <a name="line.2346"></a>
<FONT color="green">2347</FONT>            // Complete the updating of ZMAT.<a name="line.2347"></a>
<FONT color="green">2348</FONT>    <a name="line.2348"></a>
<FONT color="green">2349</FONT>            final double sqrtDenom = Math.sqrt(denom);<a name="line.2349"></a>
<FONT color="green">2350</FONT>            final double d1 = tau / sqrtDenom;<a name="line.2350"></a>
<FONT color="green">2351</FONT>            final double d2 = zMatrix.getEntry(knew, 0) / sqrtDenom;<a name="line.2351"></a>
<FONT color="green">2352</FONT>            for (int i = 0; i &lt; npt; i++) {<a name="line.2352"></a>
<FONT color="green">2353</FONT>                zMatrix.setEntry(i, 0,<a name="line.2353"></a>
<FONT color="green">2354</FONT>                              d1 * zMatrix.getEntry(i, 0) - d2 * lagrangeValuesAtNewPoint.getEntry(i));<a name="line.2354"></a>
<FONT color="green">2355</FONT>            }<a name="line.2355"></a>
<FONT color="green">2356</FONT>    <a name="line.2356"></a>
<FONT color="green">2357</FONT>            // Finally, update the matrix BMAT.<a name="line.2357"></a>
<FONT color="green">2358</FONT>    <a name="line.2358"></a>
<FONT color="green">2359</FONT>            for (int j = 0; j &lt; n; j++) {<a name="line.2359"></a>
<FONT color="green">2360</FONT>                final int jp = npt + j;<a name="line.2360"></a>
<FONT color="green">2361</FONT>                work.setEntry(jp, bMatrix.getEntry(knew, j));<a name="line.2361"></a>
<FONT color="green">2362</FONT>                final double d3 = (alpha * lagrangeValuesAtNewPoint.getEntry(jp) - tau * work.getEntry(jp)) / denom;<a name="line.2362"></a>
<FONT color="green">2363</FONT>                final double d4 = (-beta * work.getEntry(jp) - tau * lagrangeValuesAtNewPoint.getEntry(jp)) / denom;<a name="line.2363"></a>
<FONT color="green">2364</FONT>                for (int i = 0; i &lt;= jp; i++) {<a name="line.2364"></a>
<FONT color="green">2365</FONT>                    bMatrix.setEntry(i, j,<a name="line.2365"></a>
<FONT color="green">2366</FONT>                                  bMatrix.getEntry(i, j) + d3 * lagrangeValuesAtNewPoint.getEntry(i) + d4 * work.getEntry(i));<a name="line.2366"></a>
<FONT color="green">2367</FONT>                    if (i &gt;= npt) {<a name="line.2367"></a>
<FONT color="green">2368</FONT>                        bMatrix.setEntry(jp, (i - npt), bMatrix.getEntry(i, j));<a name="line.2368"></a>
<FONT color="green">2369</FONT>                    }<a name="line.2369"></a>
<FONT color="green">2370</FONT>                }<a name="line.2370"></a>
<FONT color="green">2371</FONT>            }<a name="line.2371"></a>
<FONT color="green">2372</FONT>        } // update<a name="line.2372"></a>
<FONT color="green">2373</FONT>    <a name="line.2373"></a>
<FONT color="green">2374</FONT>        /**<a name="line.2374"></a>
<FONT color="green">2375</FONT>         * Performs validity checks.<a name="line.2375"></a>
<FONT color="green">2376</FONT>         *<a name="line.2376"></a>
<FONT color="green">2377</FONT>         * @param lowerBound Lower bounds (constraints) of the objective variables.<a name="line.2377"></a>
<FONT color="green">2378</FONT>         * @param upperBound Upperer bounds (constraints) of the objective variables.<a name="line.2378"></a>
<FONT color="green">2379</FONT>         */<a name="line.2379"></a>
<FONT color="green">2380</FONT>        private void setup(double[] lowerBound,<a name="line.2380"></a>
<FONT color="green">2381</FONT>                           double[] upperBound) {<a name="line.2381"></a>
<FONT color="green">2382</FONT>            printMethod(); // XXX<a name="line.2382"></a>
<FONT color="green">2383</FONT>    <a name="line.2383"></a>
<FONT color="green">2384</FONT>            double[] init = getStartPoint();<a name="line.2384"></a>
<FONT color="green">2385</FONT>            final int dimension = init.length;<a name="line.2385"></a>
<FONT color="green">2386</FONT>    <a name="line.2386"></a>
<FONT color="green">2387</FONT>            // Check problem dimension.<a name="line.2387"></a>
<FONT color="green">2388</FONT>            if (dimension &lt; MINIMUM_PROBLEM_DIMENSION) {<a name="line.2388"></a>
<FONT color="green">2389</FONT>                throw new NumberIsTooSmallException(dimension, MINIMUM_PROBLEM_DIMENSION, true);<a name="line.2389"></a>
<FONT color="green">2390</FONT>            }<a name="line.2390"></a>
<FONT color="green">2391</FONT>            // Check number of interpolation points.<a name="line.2391"></a>
<FONT color="green">2392</FONT>            final int[] nPointsInterval = { dimension + 2, (dimension + 2) * (dimension + 1) / 2 };<a name="line.2392"></a>
<FONT color="green">2393</FONT>            if (numberOfInterpolationPoints &lt; nPointsInterval[0] ||<a name="line.2393"></a>
<FONT color="green">2394</FONT>                numberOfInterpolationPoints &gt; nPointsInterval[1]) {<a name="line.2394"></a>
<FONT color="green">2395</FONT>                throw new OutOfRangeException(LocalizedFormats.NUMBER_OF_INTERPOLATION_POINTS,<a name="line.2395"></a>
<FONT color="green">2396</FONT>                                              numberOfInterpolationPoints,<a name="line.2396"></a>
<FONT color="green">2397</FONT>                                              nPointsInterval[0],<a name="line.2397"></a>
<FONT color="green">2398</FONT>                                              nPointsInterval[1]);<a name="line.2398"></a>
<FONT color="green">2399</FONT>            }<a name="line.2399"></a>
<FONT color="green">2400</FONT>    <a name="line.2400"></a>
<FONT color="green">2401</FONT>            // Initialize bound differences.<a name="line.2401"></a>
<FONT color="green">2402</FONT>            boundDifference = new double[dimension];<a name="line.2402"></a>
<FONT color="green">2403</FONT>    <a name="line.2403"></a>
<FONT color="green">2404</FONT>            double requiredMinDiff = 2 * initialTrustRegionRadius;<a name="line.2404"></a>
<FONT color="green">2405</FONT>            double minDiff = Double.POSITIVE_INFINITY;<a name="line.2405"></a>
<FONT color="green">2406</FONT>            for (int i = 0; i &lt; dimension; i++) {<a name="line.2406"></a>
<FONT color="green">2407</FONT>                boundDifference[i] = upperBound[i] - lowerBound[i];<a name="line.2407"></a>
<FONT color="green">2408</FONT>                minDiff = Math.min(minDiff, boundDifference[i]);<a name="line.2408"></a>
<FONT color="green">2409</FONT>            }<a name="line.2409"></a>
<FONT color="green">2410</FONT>            if (minDiff &lt; requiredMinDiff) {<a name="line.2410"></a>
<FONT color="green">2411</FONT>                initialTrustRegionRadius = minDiff / 3.0;<a name="line.2411"></a>
<FONT color="green">2412</FONT>            }<a name="line.2412"></a>
<FONT color="green">2413</FONT>    <a name="line.2413"></a>
<FONT color="green">2414</FONT>            // Initialize the data structures used by the "bobyqa" method.<a name="line.2414"></a>
<FONT color="green">2415</FONT>            bMatrix = new Array2DRowRealMatrix(dimension + numberOfInterpolationPoints,<a name="line.2415"></a>
<FONT color="green">2416</FONT>                                               dimension);<a name="line.2416"></a>
<FONT color="green">2417</FONT>            zMatrix = new Array2DRowRealMatrix(numberOfInterpolationPoints,<a name="line.2417"></a>
<FONT color="green">2418</FONT>                                               numberOfInterpolationPoints - dimension - 1);<a name="line.2418"></a>
<FONT color="green">2419</FONT>            interpolationPoints = new Array2DRowRealMatrix(numberOfInterpolationPoints,<a name="line.2419"></a>
<FONT color="green">2420</FONT>                                                           dimension);<a name="line.2420"></a>
<FONT color="green">2421</FONT>            originShift = new ArrayRealVector(dimension);<a name="line.2421"></a>
<FONT color="green">2422</FONT>            fAtInterpolationPoints = new ArrayRealVector(numberOfInterpolationPoints);<a name="line.2422"></a>
<FONT color="green">2423</FONT>            trustRegionCenterOffset = new ArrayRealVector(dimension);<a name="line.2423"></a>
<FONT color="green">2424</FONT>            gradientAtTrustRegionCenter = new ArrayRealVector(dimension);<a name="line.2424"></a>
<FONT color="green">2425</FONT>            lowerDifference = new ArrayRealVector(dimension);<a name="line.2425"></a>
<FONT color="green">2426</FONT>            upperDifference = new ArrayRealVector(dimension);<a name="line.2426"></a>
<FONT color="green">2427</FONT>            modelSecondDerivativesParameters = new ArrayRealVector(numberOfInterpolationPoints);<a name="line.2427"></a>
<FONT color="green">2428</FONT>            newPoint = new ArrayRealVector(dimension);<a name="line.2428"></a>
<FONT color="green">2429</FONT>            alternativeNewPoint = new ArrayRealVector(dimension);<a name="line.2429"></a>
<FONT color="green">2430</FONT>            trialStepPoint = new ArrayRealVector(dimension);<a name="line.2430"></a>
<FONT color="green">2431</FONT>            lagrangeValuesAtNewPoint = new ArrayRealVector(dimension + numberOfInterpolationPoints);<a name="line.2431"></a>
<FONT color="green">2432</FONT>            modelSecondDerivativesValues = new ArrayRealVector(dimension * (dimension + 1) / 2);<a name="line.2432"></a>
<FONT color="green">2433</FONT>        }<a name="line.2433"></a>
<FONT color="green">2434</FONT>    <a name="line.2434"></a>
<FONT color="green">2435</FONT>        /**<a name="line.2435"></a>
<FONT color="green">2436</FONT>         * Creates a new array.<a name="line.2436"></a>
<FONT color="green">2437</FONT>         *<a name="line.2437"></a>
<FONT color="green">2438</FONT>         * @param n Dimension of the returned array.<a name="line.2438"></a>
<FONT color="green">2439</FONT>         * @param value Value for each element.<a name="line.2439"></a>
<FONT color="green">2440</FONT>         * @return an array containing {@code n} elements set to the given<a name="line.2440"></a>
<FONT color="green">2441</FONT>         * {@code value}.<a name="line.2441"></a>
<FONT color="green">2442</FONT>         */<a name="line.2442"></a>
<FONT color="green">2443</FONT>        private static double[] fillNewArray(int n,<a name="line.2443"></a>
<FONT color="green">2444</FONT>                                             double value) {<a name="line.2444"></a>
<FONT color="green">2445</FONT>            double[] ds = new double[n];<a name="line.2445"></a>
<FONT color="green">2446</FONT>            Arrays.fill(ds, value);<a name="line.2446"></a>
<FONT color="green">2447</FONT>            return ds;<a name="line.2447"></a>
<FONT color="green">2448</FONT>        }<a name="line.2448"></a>
<FONT color="green">2449</FONT>    <a name="line.2449"></a>
<FONT color="green">2450</FONT>        // XXX utility for figuring out call sequence.<a name="line.2450"></a>
<FONT color="green">2451</FONT>        private static String caller(int n) {<a name="line.2451"></a>
<FONT color="green">2452</FONT>            final Throwable t = new Throwable();<a name="line.2452"></a>
<FONT color="green">2453</FONT>            final StackTraceElement[] elements = t.getStackTrace();<a name="line.2453"></a>
<FONT color="green">2454</FONT>            final StackTraceElement e = elements[n];<a name="line.2454"></a>
<FONT color="green">2455</FONT>            return e.getMethodName() + " (at line " + e.getLineNumber() + ")";<a name="line.2455"></a>
<FONT color="green">2456</FONT>        }<a name="line.2456"></a>
<FONT color="green">2457</FONT>        // XXX utility for figuring out call sequence.<a name="line.2457"></a>
<FONT color="green">2458</FONT>        private static void printState(int s) {<a name="line.2458"></a>
<FONT color="green">2459</FONT>            //        System.out.println(caller(2) + ": state " + s);<a name="line.2459"></a>
<FONT color="green">2460</FONT>        }<a name="line.2460"></a>
<FONT color="green">2461</FONT>        // XXX utility for figuring out call sequence.<a name="line.2461"></a>
<FONT color="green">2462</FONT>        private static void printMethod() {<a name="line.2462"></a>
<FONT color="green">2463</FONT>            //        System.out.println(caller(2));<a name="line.2463"></a>
<FONT color="green">2464</FONT>        }<a name="line.2464"></a>
<FONT color="green">2465</FONT>    <a name="line.2465"></a>
<FONT color="green">2466</FONT>        /**<a name="line.2466"></a>
<FONT color="green">2467</FONT>         * Marker for code paths that are not explored with the current unit tests.<a name="line.2467"></a>
<FONT color="green">2468</FONT>         * If the path becomes explored, it should just be removed from the code.<a name="line.2468"></a>
<FONT color="green">2469</FONT>         */<a name="line.2469"></a>
<FONT color="green">2470</FONT>        private static class PathIsExploredException extends RuntimeException {<a name="line.2470"></a>
<FONT color="green">2471</FONT>            private static final long serialVersionUID = 745350979634801853L;<a name="line.2471"></a>
<FONT color="green">2472</FONT>    <a name="line.2472"></a>
<FONT color="green">2473</FONT>            private static final String PATH_IS_EXPLORED<a name="line.2473"></a>
<FONT color="green">2474</FONT>                = "If this exception is thrown, just remove it from the code";<a name="line.2474"></a>
<FONT color="green">2475</FONT>    <a name="line.2475"></a>
<FONT color="green">2476</FONT>            PathIsExploredException() {<a name="line.2476"></a>
<FONT color="green">2477</FONT>                super(PATH_IS_EXPLORED + " " + BOBYQAOptimizer.caller(3));<a name="line.2477"></a>
<FONT color="green">2478</FONT>            }<a name="line.2478"></a>
<FONT color="green">2479</FONT>        }<a name="line.2479"></a>
<FONT color="green">2480</FONT>    }<a name="line.2480"></a>
<FONT color="green">2481</FONT>    //CHECKSTYLE: resume all<a name="line.2481"></a>




























































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